When I finish a 10K race in the summer, I sweat. That is the only word for it. I would be offended if someone suggested I was perspiring. To me, that would be an insult: that person didn't think I had run as hard as I could.
We have words of both Germanic and Latin origin for many concepts in English. Because the Latin words came into English primarily after the Norman conquest of 1066, they were associated with the ruling classes. In many cases they imply a more elite activity: compare, for example, "dine" and "eat." Some people still make that social or cultural distinction. Others think it's a relic of Victorian attitudes. It often varies from one word pair to another. This can be difficult when learning English, because it's more a question of how words are used than of what words mean.