First, no one really knows all the details of Tesla, Waymo or GM's approaches. We cam make inferences based on observations, tweets (which can't actually be verified) and other available data but there's still a lot we don't know. Because it's an available consumer product, people like verygreen can hack the system and see more data to give us a better idea but there's still a lot we don't know.
Broadly there seem to be two approaches - getting hyper-accurate 'HD' mapping data so the car can navigate without processing anything and developing a human-capable system so the car doesn't need any data and can figure everything out locally. Clearly, all 3 companies are doing a mixture of the two but it appears that Waymo and GM are tilting more towards the former while Tesla is more on the other side.
The problem with the HD mapping approach is that heavily relying on mapping data to lessen the required processing abilities commits you to perpetually spending a large amount of resources to keep the mapping data up to date. Even with such efforts there will necessarily be a lag between any street level change and the mapping data, leading to issues.
I agree with
@willow_hiller - the approach Tesla appears to be taking seems to be more generalizable. It may well be that all the companies' approaches wind up coalescing somewhere in the middle. If you think about a human driver, we are able to drive in a new area but are better drivers in familiar areas because we have a 'map' in our memory and know what to expect. The same applies to a computer.