Do all traps for a cloths washer have to be in the wall or can they be under the floor?

The most common method is to drain the washer into a 2" stand pipe 36" tall. Can be in the wall or exposed. To answer your question specifically you need to give more info or a drawing. How does your drain connect to the main drain pipe below, the horizonral pipe?

The standpipe has to be taller than the highest point of fill in the washer otherwise water will come out of the standpipe if the drain doesn't run fast enough. Where the trap is positioned is irrelevant OTHER THAN you CANNOT create an "S" trap out of a "P" trap - meaning when the outflow exits the "P" it must run horizontally to the point of the air vent before dropping down.

I pretty much agree with bloo butbtherevare codes to follow . Where do you live and is this new construction or remodel.

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Do all traps for a cloths washer have to be in the wall or can they be under the floor?

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The trap can be just about anywhere as long it's correctly vented.
Here's a typical installation. Good luck, Tom