Hello Shadowlinks!
This world is not like the typical werewolf one hence there are going to be some uncommon terms used. There are a few similarities, yes. But not enough to let you just dive into it.

You gotta know some things first so here goes,

Alpha:
The leader of a pack and the strongest. Their command is absolute and ranks lower than them cannot disobey their commands even if they want to.

They exert a powerful aura depending on what level of power they have, they can control how much of this aura they exert. It is called an Alpha's Aura.

Beta:
The second in command. Similar to a Vice President, they give their wisdom and provide their thoughts and ideas whenever needed. They step in and manage the pack when the Alpha isn't able to for whatever reason.

Second highest rank in a pack. They too have a hard time disobeying an Alpha command, which is essentially a command which includes some part of the Alpha's Aura making it impossible to disobey.

Just like an Alpha, all top ranks have an Aura. The Beta has a Beta's Aura and the Gamma a Gamma's Aura and so on.

Gamma:
The third in command. They are what one would call a military general of sorts. They oversee the training of the warriors of the pack. They are also the strategist and the best warrior in the pack who lead and train other warriors.

They too exert power just like all higher ranks do which makes it impossible to disobey for ranks lower than them.

Luna:
They are the Alpha's mate/soulmate. They have the same level of power as their Alpha, they are after all their mates. Though sometimes cruel alpha's think of their mates as someone lower than them, hence leading to the Luna's being discriminated against.

They also have a Luna's Aura and you may have guessed it, a Luna command. Just like an Alpha. They alongside their counterpart lead the pack.

Some in the pack see them as a mother figure but Luna's can have whatever influence they want. They could be a motherly figure or the most badass in the pack.

Beta female:
You can tell by the name. They are the mates of the betas.

They do a similar job of a beta. But their work is comparatively less to that of a beta, they can choose to help their mates and such. In terms of power, it is equal to their mate.

Gamma female:
Same as Beta female. They are mates of the Gammas. Their work is very similar to that of the gamma. In terms of power, equal to their mate as always.

There is a catch though. Yes, all of these roles are the highest in the pack. But they aren't just handed down. Yes, when a new alpha is named or a Luna is just found and accepted, they receive a sliver of the power of a true Luna or Alpha.

After getting a bare minimum of their powers, they have to train vigorously. All of the top ranks do. They may have previous training if they are children of Alpha's and other higher ranks but that isn't always true.

Anyway, what I'm trying to say is they don't get their powers on a silver platter. They have to work very hard, train and study, learn and get knowledge. Everything matters. The more thorough your training the more powerful you are, but you also can't overexert the training, some people have naturally high potential or some just don't have that potential of being very powerful.

Moving on...

Warriors:
They have a very important role in protecting the pack.

They get trained for years until they can qualify in a test which is very important to pass. If you don't pass you can't become a warrior and have to try again next year. Each year, a new batch of warriors pass the exam.

When a warrior successfully passes, a ceremony is conducted for all the warriors where they shift again and have visible changes in their bodies depending on what they are good at, suppose a person has great speed they get an increase in speed. A person that has great strength, gets an increase in strength, and so on.

In their human and wolf form, they have an imprint on their arms, like a tattoo. Which is a sign indicating that that person is a warrior.

Trackers:
They are useful at tracking things. Their sense of smell and hearing is almost as powerful as a beta.

They help with many things in the pack, For example, a person goes missing then the pack trackers step in because their sense of smell is superior to an average wolf.

They are also very important and go through training. They too have a test like warriors and have a mark unique to trackers. They are similar to warriors too.

Pack doctor:
Rank wise they come at number 4 in the top ranks (the Alpha's mate and other top ranks' mates are equal to their mate hence they count the same rank as their counterparts).

Every single pack doctor has a minimal amount of magic to help heal injuries, though the amount of magic a person has depends individually.

Common members:
Common members are the women, children, and men, just normal people. They don't have any special ranks but they of course matter. Every single person in a pack matters. From the Alpha to the Omega.

Omegas:
They are the lowest rank in a pack. But that doesn't mean one should treat them poorly or in an inhumane way.

Though some disagree with that opinion. Evil assholes they are.

Anyway, omegas take care of the pack and the top rank's needs. The top ranks and other members of good and open-minded pack's respect them for their efforts while evil packs, treat them like trash.

How is a pack usually divided?
There is always an Alpha, a Beta, and a Gamma but the people of these ranks may find their mates at a later time in life who fill these positions Luna, Beta female, and Gamma female at a later time. Then there are the common pack members and warriors and omegas.

Ranks in a pack:
1. Alpha and Luna
2. Beta and Beta female
3. Gamma and Gamma female
4. Pack doctors, warriors and trackers
5. Common members
6. Omegas

When does a person shift into a wolf?
It's always at the age of 13 and from there on they can hear their wolf and talk to them in their minds. The wolf and their human mature together over the years and find their mates after they turn 18. It's common for early pregnancy at around the age of 20 for werewolves.

Honorable wolves respect their mates and their choices but like always not everything is unicorns and rainbows. There is always evil somewhere hidden or on the surface.