I lived in a RV that was on my own property sitting on blocks without the wheels removed and I'm fairly certain it was considered a residence as I paid property taxes which included improvements such a garage and trailer.
However I was told in order for the RV to be classified as an actual mobile home or home it would require a permanent foundation. I'm not certain of the definition of permanent foundation, as there are homes in the area built with cement block foundations, some use creosote logs with cement pads, date back to the 60's and earlier. This 44 foot RV with tires was mounted on cement blocks where the tires did not touch the ground. I installed a 240 service with panel into it, removing the exterior aluminum and rewiring the entire RV to code. It also had permanent water and sewer lines.
However I also have stayed full time in RV parks. In one park at least the county and state classify an RV space as a camping spot and not a residence. As with most RV parks property on which the RVer's rent space is business property and the land and business owner pay business property tax.
The tenants may be considered to county residence however their RV is sitting on a space that's usually considered to be for camping and not an actual permanent residence such as a home or apartment. I know people who have been living in RV parks for more than 20 to 30+ years, but technically their renting a camping spot and can move any time they want after disconnecting from the utilities designed for RVs.
The utilities for each space are not permanent residence installation. There their for people who want to rent the space from a day to a month, similar to a motel.
As for searching a vehicle I'm not certain perhaps a grey area. If able to come up with reasons and laws you can't search a persons vehicle without a warrant then perhaps they may apply however the people staying month to month for years in a RV spot may also be considered to a residence of the county, I'm not certain perhaps another grey area for lawyers to work out if a reason were to arise.
An apartment your renting the building and the land the building is sitting on as a permanent residence. In a RV park your renting the space and it's utilities designed for mobile camping and I think technically (perhaps depends on the state and county) you're camping. However a warrant may be required to search a RV even though technically a person is camping, and as I said many full timers are residence of the county the park is in as they are registered to vote, their vehicles are licensed and registered at the RV parks street and address and often with their space number. Some have telephone service, most have cell service, pay for cable or satellite, have permanently installed lpg tanks that are regularly serviced, etc., for the address of the space their renting. Their RV spot may be a billing address, address for insurance, divers license, passport, etc. very similar or the same as a permanent residence.
So it may be difficult to say some RVer's are (temporary) campers living in a vehicle on wheels even though the space their renting may be technically classified as a camp site for RVs (vehicles) and not a permanent home or apartment. Perhaps they need to change the laws to reflect how long a person been renting a RV space while living in a RV as a permanent residence.
If your on the road, you're definitely considered to be a vehicle.