A local term is a name for a body modification that is considered local to a given geographic, social, political, or commercial group, rather than one that is considered universal. Local terms tend to be known by only a small subsector of the body modification community, while universal terms tend to be known by all. As such, if a piercer is not familiar with the local terminology you use to refer to a particular piercing, this does not in any way indicate that the piercer in question is technically incapable of performing said piercing successfully.
To give an example, two local terms for the upper lip frenulum piercing are the "scrumper" (Toronto, Canada) and the "smiley" (Tel Aviv, Israel). Most piercings outside of the standards will have dozens of local names including one or two that are usually quite well known.