Are there different English words for the two types of caterpillar 毛虫 and 肉虫?
It's quite easy to distinguish between 毛虫 and 肉虫. 毛 means furry, and 肉 means meaty. If a caterpillar looks "furry", it's 毛虫. Otherwise, it's a 肉虫.

This one is a 毛虫:



And this one is 肉虫: