This is gonna be long sooooo I'mma start with the simple stuff. Most of this info will be copied from the Warriors Wikipedia page.

SEASONS
Newleaf: spring
Greenleaf: summer
Leaf-fall: autumn/fall
Leaf-bare: well there's only one season not mentioned yet so it's probably winter lol

GENERAL TIME TERMS
Moon - The time between full moons, about a month's time.
Moonhigh - When the moon is at its highest point in the sky; about midnight.
Moonrise - The time when the moon rises.
Half-moon - About two weeks, half a month.
Quarter-moon - About a week.
Sunhigh - The point during the day when the sun is highest in the sky; noon.
Sunrise - One day in cat time (i.e. One sunrise ago).
Season - A quarter of a year in cat time. Four seasons equal a year.
Heartbeat - A split second.
Claw-moon - When the moon resembles the shape of an unsheathed claw, equivalent to crescent moon.
Sundown - Dusk.
Sunup - Usually used to describe the dawn. However, Dawn is still used for example in the phrase "Dawn Patrol."

DISTANCE TERMS
Fox-length - approximately a yard, or 80 cm
Kittenstep or kitstep - approximately an inch or a half inch. (1.25-2.5 cm)
Tail-length - approximately a foot. (30 cm)
Rabbit hop or rabbit length - a foot and a half. (45 cm)
Mouse-length - two or three inches. (5-7.5 cm)
Pawstep - roughly six inches, the length of a grown cat's stride. (15 cm)[61]
Tree-length - roughly the length of a tree (around 15 m).

RANKING TERMS
Kittypet - a domesticated cat; used as an insult twowards Rusty/Firepaw in the first book, Into the Wild.
Kit - a baby cat under six moons. Their name is usually attributed to their coat.
Apprentice - a cat from six moons of age up to a year old.
Warrior - a cat who has finished their apprenticeship and has been given their new name, dropping their suffix of "paw" and replacing it with something based on their character or other circumstances.
Mentor- a cat (particularly a warrior but in certain circumstances the leader can and will fill this role) that trains an apprentice.
Queen - a she-cat that is either pregnant or nursing kits and who helps out the other queens even if they don't have kits of their own.
Elder- a cat who has left their warrior days behind them and can no longer fight due to whatever circumstances (for example, loss of sight, injuries or sickness in general, or if they're too old to continue their duties as warriors.
Medicine cat- like a herbalist for cats. They use natural remedies to cure ailments and treat pain.
Leader- self-explanatory, but it's the leader of the Clan. They are granted nine lives by StarClan at the Moonpool so they, quote-unquote, "can be first in every battle and last to take a piece of fresh-kill" which gives them basically giving them more time to serve/protect/lead their Clan.
Deputy- the leader's number two/second-in-command

LIVING SPACES
Camp - The place where a Clan makes their permanent home.
Leader's den - The den in camp that belongs to the Clan leader.
Medicine cat's den - The den in camp that belongs to the Clan's medicine cat and his or her apprentice. Sometimes referred to as the medicine den.
Warriors' den - The den in camp that is shared between the warriors and the deputy of that Clan.
Apprentices' den - The den in camp that is shared between the apprentices of that Clan.
Elders' den - The den in camp that is shared between the elders of that Clan.
Nursery - The den in camp that is shared by the queens and kits of that Clan.
Dirtplace - The place near the camp where cats go to urinate or excrete.
Fresh-kill pile - The place, usually in the center of the camp, where the warriors drop the prey they caught while hunting, so it is easily accessible to all the cats in the Clan.

((I think that's the basics))