if I create the database of my project in Visual Studio it will always use the T-SQL language to create the manipulate?
It’s not that simple. T-SQL is the default language for stored procedures. But it is possible to use other languages, you decide which one to use. And you can even not create stored procedures. If you’re not wearing it, just query uses T-SQL, but it is not easy to use something specific to it, in practice it will only use standard SQL command.
Or I can create the entire database with the relationships and everything in SQL Server Management Studio and then just connect in Visual Studio?
Yes, you can do that, one has nothing to do with the other and each serves a different purpose. Visual Studio even has some facilities to manage SQL Server, but it’s not as complete as software made just to manage it.
The reason for the question is because I had problems when I created the SQL Server Management Studio database and went to try to make relations in VS it seems that the two do not communicate because they use different SQL languages
No, this does not proceed, there is no such thing because Visual Studio is actually just a programming IDE, just like Management Studio is just an SQL Server IDE. When you go to access the database it is one no matter where you are accessing, so there is no different SQL. If you’ve had a problem it’s because you’ve done something wrong in some case.
If you can do in one of them correctly do so then.