When looking through the two tags descriptions and related questions, to me they seem to fall under the same category. They both set up a seemingly normal situation with some twist that requires outside the box thinking to come to the unique correct answer.
situation's tag wiki excerpt says:
A puzzle that involves figuring out what happened with regard to a certain incident.
This is generally how I use it (not only on my own posts but also when editing other people's, which I do a lot).
Many, but not all, situation questions are lateral-thinking. For example, A 600 foot Rope, and an 800 foot Drop and Is it always possible to balance a 4-legged table? are about explaining how a particular situation is handled, but they can be solved directly by logical thinking without requiring lateral thinking.
Very many lateral-thinking questions are not situation. For example, Find the letters that complete these five patterns or Which country is INDIA in? or Make all the statements true are all puzzles which require lateral thinking to be solved, but none of them are about explaining situations.
So no, they're not describing the same thing. Either tag can be used without the other in a reasonable way.