The help text under those settings only serves as advice for best practices. Most sites have a large and a small logo.
You can see this here on Meta. If you visit a topic page, you’ll see the large logo in the header. Once you scroll down a bit, you’ll see the small logo + the topic title and category / tags in the header.
You can use the same 120x120 image for both the small and large logos if it works for your site and you’re happy with how it looks.