Clan Ranks

Kit
A kit is a cat who has not been made an apprentice yet. Their names always end in "-kit" (e.g. Dovekit, Lionkit, Blossomkit) Most often, they are under the age of six moons, though sometimes they are held back from being an apprentice for a certain amount of time, sometimes due to injury or misbehaving. (Crookedkit) They stay in the camp and are forbidden to leave it, unless accompanied by an older cat, such as a warrior, a medicine cat, or any kind of apprentice.

Apprentice
An apprentice is a cat in training to become a warrior. Their names end in the word "-paw" (e.g. Tawnypaw, Bramblepaw, Firepaw etc). One exception to this is Boulder who opted to keep his loner name upon joining ShadowClan, and becoming an apprentice, and Egg, who kept his name upon joining SkyClan, becoming Sharpclaw's apprentice. Most usually are at or over the age of six moons. They have a mentor appointed to them at their ceremony and most days are taken out battle training or hunting. They are also given the task of cleaning out bedding and removing Elders' ticks and fleas. Apprentices are not allowed to have a mate or kits, likely because of their young age or not to interrupt their training.

Medicine Cat Apprentice
A medicine cat apprentice is the cat that is being trained to follow in the pawsteps of the medicine cat. They learn healing and spiritual lore from the medicine cat. Medicine cat apprentices also accompany their mentors in their visit to the Moonhollow every half-moon to receive dreams from StarClan.
Frequently, a medicine cat apprentice who has full training will be given a warrior name ("-paw" replaced with another ending); however, medicine cat apprentices remain apprentices even when fully trained so long as the current medicine cat is still practicing the arts.
At the time the old medicine cat either dies or steps down, the medicine cat apprentice becomes a full medicine cat, somewhat like the leader/deputy relationship. When the apprentice becomes the full medicine cat then she/he  can have an apprentice of their own.

Warrior
A warrior is a cat trained in the arts of fighting and hunting. Warriors make up the bulk of a Clan, and provide that Clan with the protection and food supply that keeps it safe and well-fed. Typically, a cat is made a warrior at or over the age of twelve moons. In their oath to become a warrior, they promise to "uphold the warrior code and protect and defend their Clan, even at the cost of their life."
Warrior dens are very often near the front of the Clan, where they can protect the rest of their Clan from attacks.
There are also senior warriors, older, respected warriors, mentioned to have a good bond with the Clan's leader.

Queen
A queen is a she-cat nursing or expecting kits. Their primary task during this time is the raising of their kits.
Some queens stay in the nursery after they have kits (e.g. Daisy, Goldenflower, and Ferncloud). They are thought to do this because they feel they can help the nursing queens. Some queens, such as Daisy, do not feel suited for Clan life aside from helping the other queens. They most often help other queens when no milk is available, or when the mother is ill/dead.
Kits are protected from attacks and the nursery is often situated at the back of the camp, away from the entrance.

Medicine Cat
The medicine cat serves the Clan as both their spiritual leader and healer, making them akin to the idea of a 'medicine man' in a tribal society. In addition to their responsibilities to their Clan, they have responsibility to one another and StarClan. They carry out their responsibilities to StarClan once every half-moon, meeting together to discuss matters privately and share dreams with StarClan. Clan leaders often rely on them to carry messages from StarClan, as medicine cats have a link no other cat has to the deceased.
As a healer, they gather herbs and dispense them as an apothecary would. They handle diagnosis and treatment of both illness and injury for all the cats in the Clan.
In their role as spiritual leader, they teach the code, interpret omen and prophecy, and generally serve the Clan as a conduit between the earthly cats and their ghostly counterparts.
As a medicine cat, they are not allowed to have a mate or kits, but this rule has been broken by certain medicine cats. Medicine cats also exist outside of typical Clan rivalries in order to treat all cats fairly.

Deputy
The deputy is the second-in-command to the leader, and may be considered an apprentice to the art of leading the Clan. They serve in the leader's place in situations where the leader is unable to fulfill their duties. They are in charge of organizing patrols and they are often called on by the leader for advice, but other than that, they retain the normal duties of a warrior.
To become a deputy, a cat must have trained at least one apprentice. However, in the New Prophecy Arc, Brambleclaw became deputy of ThunderClan without an apprentice, but he was granted the promise to train one.
Upon the leader's death, they become the leader and go to the Moonhollow so StarClan can grant them nine lives. Deputies may also retire and give up their place as deputy if they wish (for example, Tawnyspots).

Leader
A Clan leader is charged with the responsibility to watch over and manage an entire Clan, maintaining discipline, order, and protection. Leaders are normally granted nine lives and a new name with the ending "-star" (e.g. Firestar, Bluestar) in a ceremony where nine StarClan cats come to them in a dream at the Moonshollow. However, a leader may not receive all nine lives if the previous leader of his or her Clan is still alive; in this instance, a leader will have a life taken off the original total of nine for every life the previous leader still possesses (e.g. Sunstar ). Sometimes StarClan will not accept a leader (e.g. Nightstar ), if this happens then the Clan is usually thrown into turmoil.

Elder
An elder is a retired warrior, deputy, queen, medicine cat, or leader who is too old or not in suitable shape to continue with their duties. Elders are taken care of by the whole Clan, and are given respect for the time they have served as warriors. They are responsible for taking the body of a dead cat out to be buried.
Some cats don't become an elder only because of old age; if there is ever a condition which prevents the cat from fulfilling their duties to their Clan, it usually leads to the cat's decision of retiring (e.g. Longtail, Heavystep)