Replacing your strings with the same gauge usually keeps your setup the same. If you make a big change, let the new strings settle and then check how the bass plays. Adjustments to the truss rod, action or intonation may be needed.
The same goes for tunings. Moving to Drop D alone may not need a setup if the bass still plays well. Drop C and Drop B lower all four strings, so they deserve closer attention, especially combined with a heavier gauge.
Switching from nickel to stainless steel at the same gauge and construction usually doesn't call for major changes, though every instrument responds differently.
If you're unsure, have a qualified technician check your bass.