My understanding is that in many (but not all) cases they're gramatically interchangeable, but imply different levels of directness. Something like the difference between "I see you" (direct) and "I can see you" (indirect), with a general preference for the latter in polite conversation. It's not a perfect comparison because in English both usages of see are transitive, but hopefully the general idea comes across.
Circling back to the original discussion: I'd say that it's better to compare the past & non-past tenses of Japanese verbs:
- "Thank you" in the past tense ("ありがとうございました") conveys that you are thankful for acts already rendered and that you do not intend to impose further.
- "Thank you" in the non-past tense ("ありがとうございます") conveys that you are actively thankful, generally when the act in question is still in progress or otherwise not yet completely rendered.
This is a nuance that English renders trivial with a simple "Thank you", much like Japanese renders trivial the difference between a completed "look" and an incomplete "see".
Circling back to the original discussion: I'd say that it's better to compare the past & non-past tenses of Japanese verbs:
- "Thank you" in the past tense ("ありがとうございました") conveys that you are thankful for acts already rendered and that you do not intend to impose further.
- "Thank you" in the non-past tense ("ありがとうございます") conveys that you are actively thankful, generally when the act in question is still in progress or otherwise not yet completely rendered.
This is a nuance that English renders trivial with a simple "Thank you", much like Japanese renders trivial the difference between a completed "look" and an incomplete "see".