Captain in the airline sense is an honorific: something that other people call you out of respect, but it is not a title or rank. People who actually care about such things would consider it rather pompous to use an honorific to describe yourself. Most people couldn't care less
Traditionally, senior military officers can retain their rank as a title once they leave the services, but army Captains are not high enough rank to do this (didn't stop Captain Mark Phillips though). Navy Captains, on the other hand, are - so, formally, the only people that should call them Captain Bloggs are current Army officers or current or ex-navy Officers.
In the real world, you can call yourself anything you like as long as you don't attempt to obtain advantage through it, so if you want to call yourself Captain then why not? A CPL or ATPL has nothing to do with it (although you would be considered a real pratt if you called yourself Captain Bloggs if you weren't a Captain of any sort, and Captian of a C152 barely counts).