Sodium hydroxide is an ionic compound and it just dissolves in water.
NaOH(s) + water Na⁺(aq) + OH¯(aq)

Ammonia and the carbonate ion are weak bases, just a small fraction of the species reacting by proton transfer from water:
NH₃(aq) + H₂O NH₄⁺(aq) + OH¯(aq)
CO₃²¯(aq) + H₂O HCO₃¯(aq) + OH¯(aq)