The answer to this question depends on an understanding of the two distinctions: flat and round, and static and dynamic.
As pointed out, static characters do not change, while dynamic characters do. If a character is the same type of person at the beginning and the end of a story, they are static. If the character becomes a different type of person, or if our understanding of them changes due to new aspects of their personality being revealed, they are dynamic. Static means staying still, while dynamic means moving and active.
Flat and round refer to how complicated a character is. A flat character lacks detail or nuance in personality. Flat characters are identified by and limited to one or two very distinct, often stereotypical traits. Everything they do in a story, play, or novel is characterized by their flat personality. Side characters are often flat because the story isn't about them. A round character, on the other hand, is more complex and harder to simply describe as a certain type. Aspects of round characters may seem confusing and almost contradictory because they're like real people: complicated. More important characters are often round because writers spend more time building them for readers than they do with the less important characters.
So the two distinctions are not actually interchangeable although they may go together. Flat characters are sometimes also static, and round characters are also sometimes dynamic, but a character could certainly be round and static or flat and dynamic. But don't let that worry you: it's pretty simple.
Simple or complicated=flat or round.
Changing or not changing=static or dynamic.