When I go to the store to look at bettas I always grab the ones I like and put the cups next to each other to judge and compare. I find when I put the HM and Delta Tails together I find most of the time that they look the same.
So my question is: Can Delta Tails become HM's?
Pictures of the different types are recommended for this post!
NOTE: I did find this on a web page:
Delta tail was the first step before achieving halfmoon tails. Delta tails are like a fan tail with crisp, sharp angles at the tail edges - the sharper the better. If the angle is wider than 130° then it is a "super delta tail". And if the angle reaches a perfect 180° (or more) then we have a halfmoon!

The halfmoon tail is elusive because it seems to pop up in spawns, and then forever disappear. You can have 2 perfect halfmoons, breed them together and not get a single halfmoon fry in the spawn. They are rare and therefore way costly. It is a most gorgeous looking tail which, when flared, looks like a half circle, hence the name "halfmoon"