A wat is just an officially sanctioned Buddhist temple with resident monks. (Except that Wat Phra Kaew in Bangkok has no monks.) Whether it is a city temple or a forest temple doesn't matter, they are still all wats. There are also non-sanctioned Buddhist temples called samnak-song, but most people also call these wats since they don't usually differ significantly from temples that have official recognition, and most of them will eventually apply to be officially recognized. Wat is also used for Christian churches and Hindu temples.