Are there any limits for using Claude 3.7 sonnet on cursor 20$ version?

I have claude pro subscription right now, I see cursor is the same price as claude pro, I think cursor is better at viewing my old codes and keeping the design and everything consistant am I right?
I mean is the power and intelligence of Cursor’s claude 3.7 sonnet model is the same as the anthropic account?
And can I use its extended thinking mode? Fully free for 1 month? (I don’t care about slowness actually, just work)
Another question came to my mind, how much slow are we talking about?
Sorry for these weird questions I’m just new to cursor​:sweat_smile::sweat_smile: