'amel' vs. 'osek'

Question

We speak of being עָמֵל בַּתּוֹרָה (e.g., Rashi to B'chukosay 26:3 and :14) and also of being עוֹסֵק בַּתּוֹרָה (e.g., birchos haTora in the morning). What is each (especially as contrasted with the other? How do they differ)?

Sources, please, if possible.

Answer 1

My sense in this was always:

עמל connotes a struggle. for instance, ואת עמלינו. It is something that requires effort.

עוסק has the connotation of engaging in something, learning it deeply and being very involved in it.

Answer 2

To be עוסק in Torah is to make it your work - your עסק. When someone asks you "What do you do?", you should answer them "I learn Torah". Their next question will probably be how do you earn money to live, and the answer depends on your profession, but we are commanded that our business is learning Torah.

You must also put as much sustainable effort into it as you can - that is עמל in Torah.