In general, acting, such as an "acting governor" implies that the person is performing the duties of the position even though they have not been formally appointed/elected/etc to that position (and do not actually have that title). For example, if the governor leaves, the deputy governor might then perform all the governor's normal duties, in which case they are still officially only a deputy governor, but an "acting governor".
The word interim, on the other hand, usually implies that somebody does, in fact, officially have that job title, but it is only for a limited period of time until some other event (such as an election) can occur which may replace them.
(Some people do use the word interim for both cases, simply to mean "doing the job temporarily", regardless of what the official title is, though..)