Typically it's 1/4" over an unfinished drywall that might need to be taken from taped joints to finish once the drywall is removed. Usually nailed only.

A photo? If you don't like it in some areas it's better to remove and put some other material in. Usually the thick stuff is tongue and groove and will expand and contract with changes in humidity. If you paint, you may find the joints open up in winter and expose the unpainted wood. If carefully removed, solid wood paneling can be re-purposed and may have salvage value.