That's correct, most any exercise is a variation of the same theme.
Don't see the one arm DB concentration curl hyped much anymore. One of the foundation of bicep training back in the day. If believing in the mind-body connection,and preforming it in the intended way, this type curl would lead the way. Thumbs facing somewhat forward at the bottom position. Thumbs facing somewhat out at the finished, or top, position.
As would incline DB curls, where the arms are allowed to hang freely, for the full stretch, and than curled both DB's to the shoulders.The thumbs should be facing front at the start of the movement and facing outwards at the top position.. All the while the back of the head must remain on the bench it's self.
The chair DB curl, where one would sit sideways on a straight back chair, one arm hanging over a straight back chair and curl up a DB that way. Thumbs reacting the same way as above. Connect the mind, focus and physical act of curling on any of these three versions.
When allowing more of a twist to the wrist, when curling, more recruitment of the actual bicep muscle is involved. As opposed to curling a straight/EZ bar. In this case the wrist/grip is fixed in one position. One of the functions of he biceps is to twist the wrist and forearms.
Example: hold one forearm 90 degrees in front of the body, with the fingers facing down in a relaxed manner. Lightly grip the bicep with the other hand, and slowly twist the wrist until the fingers are facing almost straight up. You will feel the biceps working towards a contraction of the muscle.
All the the above is all well and good and could be in the class of pure BB'ing. If it works for you, it works for you. Just laying this stuff down for those who may be interested, and having a different slant on training.
From my own personal observations (for what their worth), one of the better mass producers of bicep mass is heavier cheating, or partial rep, BB curls. EZ bar for some. Not suited for everyone (nothing really is). To each his own, after all.
Good Luck