Big congrats on the OHP. Every advance on that lift is sweet.
And congrats on the chins, too! Now you have them going on.
You'll be looking back at the beginning of July and saying "until then, I couldn't even do one".
That was before. Welcome to after!
That "palms facing each other" grip is (I think) called hammer grip.
The main difference between chins and pulls seems to be a combo of grip width and direction:
wider (shoulder width or more) overhand grip: pull-ups, narrower (less than shoulder width) underhand grip: chin-ups.
Look 'em up to see which muscle groups they work, but pulls tend to work biceps.
Don't know much bout no hammer grips.


