What Is the Difference Between Trimble SketchUp and Google SketchUp?

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.

Trimble eventually acquired SketchUp from Google and continued its development which turned it into a very effective and very popular early stage design and rapid prototyping tool.