Say a caster wants to travel to a different continent on the same plane. Can that journey be made using the spell plane shift, or can plane shift be used only to travel to a different plane than the caster's currently on?
This is specifically answered in the spell’s description:
You and up to eight willing creatures who link hands in a circle are transported to a different plane of existence.
Nowhere does it say you can teleport to a location on the same plane of existence, so you can’t.
The caveat being that in order to travel to a different location on your starting plane of existence you would need to cast Plane Shift twice, which typically requires a long rest between castings, a 15th level caster sacrificing their only 7th and 8th level spell slots, 2 casters of the appropriate level, or some other way to cast a 7th level spell twice per day. This will allow you to a different plane on the first casting then a different location back on your original plane on the second casting.