"Base" has a more military-functional meaning, whereas "camp"
accentuates more the locality itself.
Accordingly, our naval bases aren't called as "Changi Camp" or
"Pulau Brani Camp" or "Tuas Camp" et al. Similarly, Kranji Camp or
Sungei Gedong Camp or Hendon camp aren't officially known after
their respective Formations, though you'll likely see "Home of the
Artillery/Armour/Commandos" signages inside their
vincinities.
For the army itself, the term "base" also historically denotes a
military outfit itself, usually support-oriented &
rear-echelon: eg. Army Logistics Base, SAF Ammunication Base,
Central Manpower Base, etc. Like combat units, a single CO commands
these entities at the top, & in no sense are they recognized as
Army Formations by themselves, even though they have many more
departments than a frontline unit.
In a real war, I also don't see us launching operations from the
present facilities of the various HQ Divisions or Brigades.
Instead, to complement the frontline units, IMO we'll likely adopt
the American strategy of "base camps", or field HQs that can
accomodate brigade/division elements & logistical
support.