I don't think so. I don't remember accurately but I doubt James's animagus was stag

The reason I posted this is because on the wiki it says that mcgonagalls patronus is a tabby cat, and of course her animagus form is a tabby cat. I just wanted to make sure.

Hm, not always. Becoming an animagus isn't your everyday thing and succeeding as well.

How the animal I'm your Patronus is choosen:

"Based on the fact that Patronuses are conjured by recalling happy memories, it stands to reason that a Patronus might change its form after one falls in love and the memories used to conjure the Patronus largely revolve around the person the caster is in love with. In addition, it seems that some couples have "complementary" Patronuses (male and female forms of the same animal), such as Lily and James Potter. It is, however, unknown if this is a coincidence or not. If a wizard is an Animagus and can summon a corporeal Patronus, the two may take the same form, as was the case for Minerva McGonagall and James Potter.[12] Remus Lupin's Patronus takes the form of a wolf, rather than a werewolf; whether or not all werewolves would generate a similar Patronus is unknown. It stands to reason that it's likely due to Remus' best memories of his youth revolving around the acceptance he felt despite his condition, in which he felt more at home in his wolf form during those times, rather than cursed by it and also due to his nature as desiring a sense of belonging at his core, much like a true wolf.

Most Patronuses take the form of an ordinary animal. Magical creatures, such as Albus Dumbledore's phoenix Patronus, are uncommon. It is extremely rare for Patronuses to take the form of extinct animals. Hedley Fleetwood's Woolly Mammoth Patronus is a notable exception.[6]Andros the Invincible was the only wizard capable of casting a Patronus the size of a Giant,[21] although whether it was a giant or not is unknown."

An animal for the animagus:

"An Animagus could not choose their animal form. Rather, one became the animal which suited them best.[10] It may be that a wizard's Animagus form was always the same as their full-bodied Patronus; Minerva McGonagall was one such case, both being a known cat Animagus and having a cat Patronus.[11] Apparently, the form one's Patronus took may have been determined by the same inner-traits as the Animagus form.

An Animagus in animal form was not restrained by the usual lifespan of the animal they were. Animagus Peter Pettigrew lived as a rat for at least twelve years, despite rodents normally living at most a few years.[12]

Each Animagus bore an identifying mark on their animal form that was caused by some visible trait on their human body. This could be physical, like their dental structure, or acquired, like glasses. Both Minerva McGonagall and Rita Skeeter had markings on their Animagus forms caused by their spectacles. If an Animagus underwent a major physical change, such as the loss of a limb, their animal form would reflect that, as in the case of Peter Pettigrew missing a finger, and his rat form missing a toe.[12]

An Animagus could consciously choose if they also wanted to transfigure their jewellery and clothing with them."

Like u had to write a full article, couldn't u just summarize it?

Not really

@Ventaceanwastaken well, it's not even the full article on the wiki, it's just a section sourced with the maximum information which makes understanding it easy :)

They can be the same, but they don't have to. I mean McGonnagals Patronus was multiple cats (I know the grammer is a bit off but it's one Patronus so, let's go with singular)

I learned a lot more here than at school.