What is the common everyday term for people with front teeth moving forward?

"Buck-toothed" would be quite insulting if used to describe somebody. It also specifically means that the teeth are angled forwards, protruding. Another term for this is an overbite (eg "she has an overbite").

The people in the photographs don't look like their teeth are angled forwards - they simply have prominent (not protruding) teeth. We might say of them that they are "toothy", meaning their teeth are a prominent part of their facial features. We might also say they "have a toothy smile". People who show a lot of their gums when they smile are sometimes called "gummy". Again, all of these could be considered insulting as they are passing comment on a person's physical features.