To make an attempt vs. to attempt

As far as I understand, to make an attempt and to attempt mean the same thing, but I’m pretty sure there’s still a difference between them that I don’t know. Does make an attempt put more emphasis on the thing you’re attempting than attempt? Does a person who makes an attempt to do something imply that they’re are putting more effort than someone who’s just attempting to do something?

(As a side note, I think some of this also applies to other similar phrases, such as make a decision and decide, take into consideration and consider, have a reaction and react, etc.)