The table on the Thailand wiki page is incomplete. It currently suggests that city municipalities (เทศบาลนคร - thesaban nakhon) be tagged as place=city and town municipalities (เทศบาลเมือง - thesaban mueang) be place=town. However, the entries for commune/township municipalities (เทศบาลตำบล - thesaban tambon) and subdistrict administration organisations (SAO; อบต. - o bo to) are still question marks.
By definition, thesaban tambon should have a population of over 5,000 (although many don’t, according to Wikipedia). Most probably have less than 10,000 or they would already have been upgraded to thesaban mueang. This range (5,000–10,000) falls within the wiki’s definition for place=village (between 1,000 and 10,000 inhabitants). However, place=village is already being used in Thailand for muban (หมู่บ้าน), which are much smaller (average population being 746 in 1990, according to Wikipedia).
The simplest solution seems to be to tag both thesaban mueang and thesaban tambon as place=town. This isn’t unreasonable, since the population threshold for city municipality in Thailand (50,000) is already lower than the general OSM guideline (100,000). However, we lose the distinction between the two by doing this. Another option would be to use place=hamlet (see below) for muban instead, freeing up place=village, but this might be more work than it’s worth.
SAOs seem somewhat trickier. They often aren’t contiguous populated places, but cover many muban within an area usually corresponding to the administrative tambon. Since tambon should already be tagged by administrative boundaries (not yet done in most areas), tagging SAOs separately seems somewhat redundant. Until tambon boundaries are available, though, they should probably still be tagged with place=something.
I’d also like to note that using place=hamlet for communities (ชุมชน - chumchon) as currently recommended conflicts with the tag’s description, i.e. “for an isolated settlement”. Since chumchon are part of incorporated municipalities, place=neighbourhood would be more appropriate.
Edited: capitalisation in title