emersed are grown in damp condition above the water line usually with the roots or some of the plant still in the water or at least water logged mud. Immersed are grown fully under water. Some larger plants will grow immersed and then when they get above the water line will grow emersed. Since the immersed plants have adapted their leaves to underwater conditions they usuaully already adpated unless there's huge water parameter like moving from a high tech to low tech tank. Depending on your tank setup you might get some melt, lots of melt or none at all with either type.
Plants that have been growing underwater don't travel so well in the post but, if you are just moving a plant from one tank to another then they transplant very well, as long as the plant is only out of the water for a short time.
Commercially grown plants that have been grown out of water do travel well, but more often than not, loose the majority of their leaves when submersed underwater.
In a well set up high tech tank, most plants will start showing new leafs before the old ones melt away!