The most common tool used to catch tubulars is the Overshot.
Overshot is an external fishing tool, which mean it catches on the outside of DP/Tubing.
Overshot catches by using something called “Grapple” which has slips that grip/bite around the tubulars and prevent slippage.
Grapple could be Spiral or Basket grapple.
Their use depend on the maximum catch size of the overshot.
There are classification of Grapple could be full strength, Slim hole, Short catch.
Here is a video of how the overshot catch and release from tubular.