A dry buckle is when the pipe wall is not broken, i.e there is no water in the pipe.
A wet buckle is when the wall is broken and the pipe is flooded.
Dry buckles are easier to overcome. Pull out the pipe cut off the buckled section and start again.
Wet buckles are usually a problem as the pipe is too heavy to pull out without breaking again. Internal plugs or external sealed clamps are possibilities followed by dewatering.
I thought a dry buckle was a buckle caused above the water line by bending the pipe too much, whereas a wet buckle was the same but, becaue it's underwater, there's external pressure on the pipe so the buckle can run, propagating along the pipe until it either reaches a point where the external pressure is less than the buckle propagation pressure or until it hits a buckle arrestor? However, it is some time since I was a pipeline engineer, so I may be wrong!
I remember putting buckle arrestors on pipe on a lay barge every 5 doubles, but I never put any on any onshore lines I built.
