I think that's exactly right. I say "try to" in more neutral situations, or noncommittal, or pessimistic. It conveys it's not my top priority to succeed. "I'll try and get it done today" is easy to imagine with a neutral tone or a downward tone, conveying that I may not get to it and it isn't my top priority. "I'll try and get it done today" is easier to imagine with a chipper tone, it's a higher priority for me, I intend to get to it.

This makes logical sense too, doesn't it? "Try and" implies success. I'm not actually saying "I'll try to get it done and I will get it done", if that was the case I'd skip the try, but I am evoking an idea in that direction.