Actually, I'd like to point out how this is wrong and why PLD and WHM currently suffer the most for being different.
A PLD brings heavy mitigation to the raid, but mainly deals in physical mitigation.
A WHM brings heavy healing output, AoE and single alike.
However, the content is balanced and focused around bringing any job and composition into a fight. Most of the player base is merely concerned with pushing out as much DPS as possible (again, keep in mind that all content is balanced around any composition, with Yoshi having even said nothing requires healers to DPS to complete it while specifically mentioning savage).
Unfortunately, PLD lacks in DPS in comparison to WAR and DRK. Even though SE has said they will not design fights that require specific roles [anymore], they went out to create Alexander 12 Savage. Bringing a PLD actually leaves them with not enough cooldowns for magic damage and they will eat Punishing Heat raw somewhere in the fight. Please, do not confuse this with doing things to specifically by-pass mechanics as they are intended. I know many do not like warrior to MT on Zurvan EX because the timing for Holmgang on Demon Claw/ Wave Cannon is tight (it's not impossible, just very, very, VERY tight). However, the intended mechanic is not dissimilar to Ser Zephirin's javelin in Thordan's Reign, minus the raid wipe on a death from a single person.
The same mentality to applied to WHM via the community. There is no need for heavy healing and being more difficult to sustain DPS (possible, not as impossible as people claim it to be) and lacking the raid utility of AST (read: number bloating from cards), it has lost it's place in the meta. Meanwhile, SCH's place is secured having a companion with infinite MP and easy MP management, even though it has the least DPS output of the three healers. Oddly enough, double AST is a thing because, again, all of the content was created around being able to bring anything (AST in regen or shield stance).
This is all the more evident in this current raid tier. There is also no point for them to fix it and may be watching and weighing what needs to be fixed and where for Stormblood (hopefully). While I enjoy each job being specialized, in PLD and WHM's cases, their specializations have been deemed unneeded (and this same stigma has been passed onto MNK for, again, lack of DAMAGE raid utility).
If we're simply looking at what skill does what, yes, the classes are the same in the case of tanks and healers. Of course they need similar skills to fulfill the same role- this is called a kit. However, the application in the meta is what makes all the difference.