Disclaimer: not played WoW since the end of WoD, but as far as I know the healing has changed very little.

I was a hardcore raider healer in WoW. FFXIV's healing is very different.

The mana efficiency of healers in FF far outpaces WoW, so that allows FF healers to weave in dps. Healer dps is very effective in FF but it hits like a wet noodle in WoW. In WoW unless you have specific healing/defensive/mana gaining mechanics that use dps abilities, there is little to no reason for healers to dps in combat as it's a waste of precious mana and a gcd wasted on stupidly low numbers. (unless you greatly outgear the content)

Additionally out of combat hp and mp regen is several times faster in FF, so there is far less downtime between pulls. If a tank doesn't wait for you to regen mp in WoW you may need all the mana you have for just healing, whereas in FF due to the higher rate of mp regen you are more likely to have a higher percentage of mana at the next pull which leaves more room for dps.