Reboring and relining are different processes. Reboring involves reaming out the barrel to a larger caliber, then re-rifling the barrel. The new caliber bore diameter must be large enough to clean out all the old rifling, while being small enough that the barrel remains thick enough for safety.
Relining also involves reaming the barrel, but the rifling is not recut. Instead, a thin-wall liner is inserted into the barrel and soldered or glued in. The liner has the rifling cut in it. Since liners are fairly thin, and the glue or solder does not give good support, they cannot be used with high pressure cartridges, and lining is limited to cartridges like .22 RF, .25-20, .32-20 and the like.
(A third method is used when it is necessary to preserve original barrel markings, but where it is desired to fire high pressure rounds. It involves reaming the original barrel to a thin shell and installing a barrel thick enough by itself to contain the pressure. This is a very precise process and one done by few shops.)
Jim