The basic elements of a set-up are:
- Relief: Truss rod adjustment
- String height: Saddle heights and radius
- Intonation: String length
In addition, the nut slots may also be adjusted for width and height.
If the new set of strings is the same brand and gauge as the old strings the intonation must be checked. It will probably require a touch up.
If the new set of strings is from a different manufacturer, is of different material or construction, or they are a different gauge set everything must be checked. It is probable that the relief will change necessitating a truss rod adjustment. If the truss rod is adjusted it is likely that one or more saddles will have to be adjusted for string height. Any change at the saddle will require tweaking the intonation.
That's a new set up.
The remedy is to always have a second set of strings in stock. Doesn't do any good now but it is a good idea for the future.
Two is one and one is none.