There are 2 modes to climb, OP CLIMB and CLB (well 3 if you include VS+xxxx).
Only difference between the 2 is CLB will meet any altitude constraints and OP CLIMB will climb straight to the selected altitude. If in CLB and ATC says unrestricted climb you would pull OP CLIMB and ignore the Alt Const.
However if you're off the lateral nav route (off the FMGS flightplan ie in HDG no NAV) CLB is unavailable so you can only use OP CLIMB (VS+xxxx).
Generally managed modes are used. Short term changes made (Selected speed/heading/alt) on the FCU are used for shorterm adjustments (eg ATC/weather).