CC-EDICT definition: to attract / to incur
Her actions drew criticism from her superior.
You will bring the blame of others upon yourself if you fail in this.
CC-EDICT definition: to give rise to / to lead to / to cause / to arouse
The news aroused much fear in Germany.
His words roused a great rage inside her.
It looks like, in the above examples, 招来 and 引起 can be swapped without changing the meaning. I don't see a meaningful distinction. I encountered 引起 first in my studies, so I expect it's more common.
Question: What's the difference between 招来 and 引起?