I have a question about the difference between verb "start" and verb phrase "start up". According to these definitions for "start" and "start up" in this dictionary, these sentences:
1a. The rain started.
1b. The rain started up.
2a. The engine started.
2b. The engine started up.
, are pretty much the same. But to native speakers, does "start up" have some other meaning not captured by "start" and vice versa ?