Keywords/terminology for using "extra" information in search problems?
Such search algorithms would generally be called informed search algorithms (or methods, techniques, etc.), or simply heuristic search algorithms. We might also call them guided search algorithms.

An example would be A* search, which uses precisely what you call "airplane distance" (more commonly referred to as the straight-line distance) as a heuristic.

Best-first search techniques would be somewhat closely-related, but they may have a slightly different meaning (they may, for example, use statistics / information gathered earlier during the same process for guidance during a later part of the search process, rather than heuristic domain knowledge given a priori).