Does a climbing creature fall when affected by Hideous Laughter?

Question

A creature is climbing on a wall, and fails a save against hideous laughter. The spell states:

A creature of your choice that you can see within range perceives everything as hilariously funny and falls into fits of laughter if this spell affects it. The target must succeed on a Wisdom saving throw or fall prone, becoming incapacitated and unable to stand up for the duration.

Does it make a difference, if the creature has a natural climb speed, vs a creature that is climbing using an Athletics skill check?

There is a similar Q&A, but it is for Pathfinder. There also is a Q&A for when the creature has spider climb, which provides a natural climb speed (but may differ from skill-based climbing, and spider climb as a spell offers additional benefits of not needing your hands).

Answer 1

Only if the DM decides it does

There is no explicit rule in the game which states that becoming prone would make someone fall if they were currently climbing, and it's not an automatic direct consequence of any of the text in the prone condition itself. It'd be a consistent interpretation of the rules that being prone, whilst climbing, reflects a state of being off-balance or barely holding on but not quite falling.

Contrast this with the rules for flying movement, which do explicitly state:

If a flying creature is knocked prone, has its speed reduced to 0, or is otherwise deprived of the ability to move, the creature falls, unless it has the ability to hover or it is being held aloft by magic, such as by the fly spell.

The fact that this is stated with regards to flying movement but no equivalent rule exists for climbing lends support to the reading that being prone doesn't automatically cause a climber to fall.

This also appears to be the reading arrived at by the designers. As we all know, Jeremy Crawford's tweets aren't official rules clarification anymore, but he was asked about this in 2017 and responded:

No general rule causes a climbing creature to fall if knocked prone. As DM, I'd look at the environment and decide. #DnD

So the designer interpretation here is that it's not an automatic consequence of the rules, but it's within the DM's purview to judge that in any particular situation, becoming prone might have the additional consequence of a dangerous fall.

In my personal judgement that might vary depending on the creature in question, and how exactly the prone condition was inflicted. Becoming prone because of hideous laughter is a much gentler experience than becoming prone because Bob the Battlemaster hit you in the face with a hammer and a trip attack, for instance.