Adding new contact to an account? And difference between account and company?

Adding new contact to an account? And difference between account and company?

We're trying to organize all of our customer contact information. 

B2B customer has account X with contact John Doe

We have a contact named Jane Doe that we want to associate to this account X, but within the account we can't do that. There's no + button next to contact but there is with just about every other module on the left side.

How can I add this contact to this account?

Also, what is the difference and / or purpose of having both account and company fields?

Thanks!