Hi Dariana,
A smirk is similar to a grin, but the main difference is usually that a smirk is half hidden. It's not hidden enough to not actually be a kind of smile, but it's not a full grin, with the face beaming. A smirk can often be irritating or conceited, and can often be related to gloating over some kind of victory.
A grin, on the other hand, is simply when a person is smiling, big and broad across their face with no attempt to hide it at all.