Caesar's "Germans" were almost certainly Celtic/Gallic - "Celtic" cultures and tribes stretched from Iberia in the west to Galatia (Anatolia) in the east.

I'm sketchier on where the Angles/Saxons/Jutes came from before they emerged into the historical record in modern-day northwestern Germany, Denmark and the Netherlands. Whether they were a reconfiguration of the tribes that had been there since time immemorial, or were groups previously to the east, displaced westward as a ripple effect of the great migrations out of central Asia.

I can't find the sources right now, but I think linguistic studies have confirmed that the celts and germans could not have come from the same origin. My impression has always been that the celts were the original inhabitants of western Europe and the British Isles and the Germanic/Nordic tribes slowly conquered and assimilated them into their culture.

I am not a historian of course. Would love to hear counterpoints; I'm interested in historical facts not propaganda :) .

Speaking of "original inhabitants" of the British Isles there was a fascinating Time Team special that mentioned that there were 7 waves of human occupation of Britain - with each of the previous six waves completely dying out.

The bigger question is whether the Belgae, who were in southeastern Britain when Caesar arrived, were Celtic or German.