Try to do something, you might or might not do it. “I’m going to try to persuade them to decide in my favor.”
Try and do something, you expect to get it done one way or another. “I’m goin down there to try and straighten them out.”
I don’t have a long history of research in this going back to the 1500s, but I grew up in southeast Texas, and this is how I’ve always understood it to be used around here, when it is used with any intention at least.