I would refer to these differences as accents as well.
It's worth noting that your examples center on differences in pronunciation for two words: got and babe. Even in the U.S., you will find differences in how words like that are pronounced, and we refer to those as regional accents.
In the U.S., there is (this is not meant to be an exhaustive list):
The northeast (or Bostonian) accent, characterized by the way they pronounce (or some would say, don't pronounce) trailing r's. The classic test for this accent is: Go park the car in the yard. If you want to hear it, have a listen to Billy Baker on YouTube.
The upper Midwestern (or Minnesota/Wisconsin) accent, characterized an slightly elongated long o sound. Do you know how to row a boat? (For more examples, you can watch Fargo.)
The Southern accent, which is hard to describe in a sentence or two, but you can read more about it on Wikipedia, or hear samples on YouTube. I have a coworker from Tennessee, and I'm reminded of his origins every time he asks for a pen, because it sounds like he's asking for a pin.
In short, just like you can often tell if a speaker hails from the U.S., the U.K., Canada, Australia, or India just by a speaker's accent (yes, accent is the word you're looking for), you can also sometimes tell what region of the U.S. a speaker is from.
Some people keep their accent all their lives; for others, it will change based on where they currently live. I'm originally from the northeastern U.S., and my first job moved me to the Nebraska, which is in the dead center of the continental U.S. I went home on vacation, and was talking to an old friend of mine. All of a sudden, he started laughing, even though I wasn't saying anything funny.
"What are you laughing at?" I asked.
"You have an accent now!" he answered.
I replied, "Well, either I got one, or I lost one – it depends on your point of view!"
If you're interested in this kind of thing, you might enjoy a visit to Forvo.com, where speakers from all of the world pronounce words one at a time, sometimes with surprising variations. Root beer, anyone? Yeah, baby!
A Wikipedia article on English accents says this about what you call AmE:
The United States does not have a concrete 'standard' accent in the same way that Britain has Received Pronunciation. Nonetheless, a form of speech known to linguists as General American is perceived by most Americans to be "accent-less", meaning a person who speaks in such a manner does not appear to be from anywhere. The region of the United States that most resembles this is the central Midwest, specifically eastern Nebraska (including Omaha and Lincoln), southern and central Iowa (including Des Moines), parts of Missouri, Ohio and western Illinois (including Peoria and the Quad Cities, but not the Chicago area).