The care system is a way of caring for the various magical people within the magical world. There are 3 organizations AMS, BCS and the OSS. Not all of them have their own hospital but what services they do offer varies from country to country. Often BCS is attached to the main area hospital. With AMS and the OSS both being small clinics. But it can vary due to the need in that area.
Two examples of this are England and Greenland. In England, the BCS is attached to Saint Mungo's. The service itself acts more like a counselling group and monitors people who might need help. They also run small clinics for magical creatures that the Ministery will not let be treated at Saint Mungos like Werewolves. The OSS and AMS both have small clinics to treat their people only. The OSS has theirs in a block of Terrace houses they have knocked together, spelled and taken over. The AMS, by contrast, has a large field with several purpose-built buildings.
Greenland, on the other hand, is one large hospital with small wings dedicated to the different organizations. These allow the people who need to stop over to do so but still be safe and can be closed off or guarded as needed. This is due to Greenland being smaller than England.
AMS stands for Aristocracy Monitoring Service.
BCS stands for Bureau Counselling Service.
OSS stands for Oxford Support Service.
Each one takes a specific type of wizard. Which type of wizard is determined on by both their gifts and their family history. This is known as the departments. There are three departments. The Old family department, the Creature department and the gift department. Which you go into is decided by an order of precedence.

The Creature Department

The creature department is ranked first and is the department that the British Wizards tend to ignore. In this department, the AMS takes the Alpha or dominant creatures. OSS takes the Omega or submissive creatures. Lastly, the BCS takes the creatures with the rare type of Beta such as Werewolves.

The Gift Department

Next is the Gift department. British wizards like to believe that this department comes last. They believe that family is more important and comes first. This department is important as each organization looks after different gifts. This is due to some gifts, such as being a sensitive, need specialist care that one organization provides. However, if you are a magical creature you fall under the creature department. All magical creatures have gifts. To deal with this all the organizations have at least someone with basic training in each gift. The different organizations just specialize in a few gifts each.
The AMS specializes in gifts such as Beast Speakers, Parsletounge, Shadow walking, Teleportation and Telekinesis.
The BCS specializes in gifts such as Natural Animgus, Metamorph, Elemental Magic, Invisibility and the ability to make yourself Transparent.
The OSS specializes in gifts such as being sensitive to magic, Seers, seeing magic, Empathy and Telepathy.

The Family Department

The last department is the family department. This is the department that British wizards see as the most important, and ranked first. Despite this belief, it is actually ranked last. This is due to the fact that it is your gender, and blood status, that determines which organization you fall under. AMS takes old family or pure-blood males even if their family are called blood traitors. Such as most of the Weasleys would fall under this organization. The OSS does the same with the females. Going with the theme the BCS takes everyone else and is the largest organization.

The Spell

Most people will fit into more than one department and even more than one Organization. Even more so if that person was a werewolf or magical creature. As such a spell was created to decide which organization a person would fall under. This spell is embedded with a complex arithmetic equation. The equation calculates which department you would fall under. It starts with are you a creature. If you are then the spell stops scanning you and you are placed into an organization. That organization would simply have to cope with any of your gifts.

The spell next scans for your gifts and sees which are strongest in you or would affect you the most in life. If the spell finds a gift that would affect you strongly then you are placed in that organization. If the spell does not see any gifts that would affect a person strongly then they will be placed under the family department based on their gender and blood status.

To know which organization you fall under the spell is cast. Someone qualified will cast it on you and you will glow the colour of that organization. AMS will glow red, BCS will glow yellow and the OSS will glow orange. It is up to the organization to work out and decided which department that person falls under. Not many remember the spell being cast on them as it is done so when the child is 2 years old. However, particularly in England, there are those that prefer their children to be under one particular Organization. They will bribe the ministry official to record the child wrong. This is dangerous, illegal and can affect the child's health. However, sometimes it is other people who record a child wrong for various reasons.

Examples.

They might be a half-blood but with gifts of being a beast speaker and able to see magic. This would mean they could fall under all the Organizations. However, due to their ability to see magic they would fall under the OSS. The ability to see magic would need training and is classed as a minor sensitive. Using lots of magic to heal that person is detrimental.

Another example you might be a female that had a gift of Teleportation and belonged to an old family. They would be placed under the family department within the OSS. As once they learned to control their ability to teleport, they would not be affected.

A third example is you might be a male with a gift for Telepathy. Again they would need to learn control. But once they have the gift would not affect their ability to be treated in a magical manner. So they would be placed under the Family department of the AMS.

How do the gifts effect someone.

How much a gift would affect a person depends on both what the gift is and how strongly it is tied into magic. A strong magical gift will mean it could be dangerous to treat a person magically. There are ways to minimise this such as the person going through regular purification baths or showers. However as much as possible, it would still be better to save the strong concentrations of magic to treatment. Rather than to find out what is wrong with them in the first place.
When the Organizations were set up a study was done to find out which magical gifts caused someone to become ill when magic was used to treat them. These were then placed under the OSS who discovered using magic on magical creatures when they were pregnant harmed the child. Not all the gifts under the OSS cause this phenomenon. The gifts that do however are Sensitive, being a seer and the ability to see magic. These are the gifts the spell scans for first.
The next five are effected on a smaller scale. Empathy, Telepathy, Elemental, Metamorph and Natural Animagus. Empathy and Telepathy fall under the OSS due to the style of gift they are. Metamorphs and Natural Animagi are most often fine with large quantities of magic. However, this is only as long as they are in their natural form when being healed. As such they fall under the preview of the BCS. This is despite them really only being seen in old families. Elemental falls under the BCS as in highly destressing situations it can cause someones elemental magic to go out of control. All major hospitals have elemental suppressing wards over them for this reason.
The next lot is Invisibility, Telekinesis, Transparent, Teleportation and Shadow Walk. This is the biggest group. Non are really affected by healing magic. The BCS has the purview for Transparent and Invisibility. Those gifts are often seen together and can occasionally cause magical health problems.
Teleportation and Shadow walking come under AMS as they are other methods of transportation. Shadow walking is most often seen in Vampires and is rare in a human. Telekinesis is another that once you have control does not affect your ability to be treated with magic.
The last group of gifts is Beast Speaker and Parseltongue both of which are languages. Therefore they are not affected at all in any way.
AMS takes the people least affected by magical treatment options. They occasionally will treat a dominant creature non-magically but it is rare for them to have to do this.