According to Kuno stative transitive predicates take ga for object marking, so nihongo ga wakaru; eigo ga dekiru; okane ga hoshii; Yasuko ga suki da; kore ga tabetakunai; etc. This ga is different than the ga for subject marking.
Now, there are basically three patterns for marking subjects and objects with these types of predicates, and it's claimed that they all stem from one source: NP-ga NP-ga stative predicate. The variations are NP-ga NP-o pred. and NP-ni NP-ga pred (NP = noun phrase). Each can be used in certain situations but not others. The point is, both watashi ga ringo ga tabetai and watashi ga ringo o tabetai are perfectly good sentences (I'm not sure about watashi ni ringo ga tabetai, though, but my guess is it's not acceptable). As far as what the difference is, Kuno says that with the ga version you're taking the noun phrase to be the object of the derivative as a whole, which are stative by assumption; with the o version, the noun phrase is taken to be the object of only the verb stems, which are action verbs. I'm not sure how much that means to you, but it doesn't really seem to help to much with how to interpret them.
As for the difference in interpretation, it says in "A Dictionary of Basic Japanese Grammar" that the ga version shows a higher level of desire, where the o version shows a lower level. It offers these sentences as examples: [Situation: The speaker has just run five miles] watashi wa mizu ga/?o nomitai. (The ? means the sentence is questionable) [Situation: The speaker has been told by a doctor to drink as much water as possible. That is, he feels he has to drink water] watashi wa mizu o/?ga nomitai ga... (implying that his stomach won't accept any more). I'm not sure how true this is; we'll have to ask some native Japanese speakers how they feel about it or read some more recent works on the issue (ADBJG is copyright 1986 and 1989).