Check behind turn/call river vs. Bet Turn/check behind river (HU)

[511 Peas]

<u>Check behind Turn/call river vs. Bet Turn/check behind river (HU)</u>

These two similar lines (cost-wise) are oft mentioned in 6-max posts.

Tell this noob when and in what situations/circumstances we're more inclined to use one versus the other (in the example of a heads-up confrontation on the turn and river, obviously)

I understand that the BetT/Check(behind)R line allows us a free showdown of sorts, and the Check(behind)T/CallR can induce a bluff- is that mainly it?

NOTE- FOR THIS QUESTION, ASSUME WE'RE HEADS-UP AND ON THE BUTTON (closing all action)

Finally, a sincere thanks for your assistance.