There was a library called the STL that is now, with modifications, a part of the std library. So in a sense you could say that the STL is a subset of the std library, or that it was an inspiration for part of it, but many people just use the terms interchangeably.

So, what that read me says is correct, it is also called the STL. If you want to be precise you should probably only call it the std library though. There are still implementations of the original STL around separate from the std library, so keeping the distinction is probably still wise.

Also to complicate things, some people use the term STL to refer to the specific parts of the std library that are from the original STL. Those pieces are containers, algorithms, functions, and iterators I think.

tl;dr it's all a mess and people say the two meaning different things all the time.