The terms "Travis Picking", "Cotton Picking", "Carter Style"... are usually used, not to describe a carbon copy of Merle, Libba or Maybelle, but a general impression.
I've often heard playing described as "Travis style", even though it is played with 3 fingers, no muting and no thumb pick. The alternating thumb bass and melody picked by the fingers is what is meant.
Very few people play the alternating bass with the fingers and treble melody with the thumb the way Libba did, but they can get a good approximation of her style playing right handed using 2 or 3 fingers.
I don't consider pattern picking to fit into either of these categories, bur I have heard people use the terms for this.
Carter style is played with the thumb and nails of the right hand, but a close approximation is possible with a flat pick.
John Hurt didn't mute the bass strings like Merle Travis, but his style had certain similarities. Perhaps "finger picking" is a good term for these styles of playing.