I would have assumed "putter" (in this sense) is onomatopoeic, from the sound of a small engine running slowly. "Potter", OTOH, comes from a word for poking or

I would have assumed "putter" (in this sense) is onomatopoeic, from the sound of a small engine running slowly. "Potter", OTOH, comes from a word for poking or prodding at the ground (hence appropriate for gardening). (I suppose with the right kind of ride-on mower, it's possible to "putter about the garden" with appropriate sound effects!) Checking OED citations, though, it seems the "putter" form (as a variant of "potter", distinct from the sound of an engine "puttering") does have a similar history (both go back to the 1820s). Still, I'd agree that "potter about the garden" is by far the more common usage.