It gets tricky when you start mixing vehicle registration with revenue sources.
This state does not even require us to register or tag privately used trailers, rather it allows the county and school district to tax them as personal property. If we want to avoid the property tax, however, (or avoid the hassles associated with trying to pull through other states untagged) we have the option to tag a trailer as an unmotorized vehicle and pay the tag fee to the state rather than the property tax to the county.
Completely different rules, tags and tax liabilities for commercial or agricultural uses. I do know that our taxes on commercial trailers are low enough that some Kansas operators establish a presence here so as to tag here.