You will get better support because of the manufacturer's and our combined efforts. Most software vendors offer direct support regardless if you purchase from them or not, but if purchase directly from thesoftware manufacturer then only their own service will be available to you.
There is no difference between Google SketchUp and Trimble SketchUp.
Google originally purchased the program in order to have everyone model their own neighborhood and upload this data into an online database so people could explore what else was happening around them on Google Earth or other means of accessing information about different places across our world. The project never really got off the ground and SketchUp became instead a very effective tool to quickly draft complex designs.