let me start off with saying this: this is not Final Fantasy, don't think it is, or you will be disapointed. WoW is a unique, innovative game that, IMO, blows FFXI out of the water in all aspects.
So, let's answer this with that fact in mind. In FFXI:
WHMs were straight healing, little bit of group buffing ability, but not up to bard level. they were also the people movers of the game.
BLMs were straight damage. no tricks, just blasting, and were the parties ride home after a hard grind.
RDMs were first and foremost enfeeblers, with a bit of buffing on the side, excluding refresh. They were also walking mana batteries should the WHM or PLD not be able to heal for some reason.
SMNs were gimped. they whipped out a pet for about 10 seconds, and were laughed at if they didn't sub WHM.
In WoW:
OK, I don't know how Shaman and druid work, as i have not played them first hand, so please correct me if i am wrong on them.
Shamans are very close to bards in that they use AoE effects for most all of their actions, and serve well as a groups healer should a priest not be available.
Druids are what most similar to early level RDMs, in that they do a bit of everything, but they can't do everything at once (no healing in bear form, no tanking in cat form, ect.) They heal as well, but i'm not sure which is the dominant healer between Druids and Shamans, my guess would be shaman, though.
Warlocks are what summoners should have been in FFXI. They summon pets, their pets do their bidding. having a pet doesn't drain mana. The pet is used to fit the situation, such as using your voidwalker to tank, or your succubus for damage. The warlock themselves focus almost entirely on DoT, having very few direct damage spells (get used to shadow bolt for direct damage, cuz that's all you got for the first 20 levels). They are also walking mana batteries, but they can only use thier mana regen powers on themselves.
Priests are the ultimate healers in this game, similar in a fashion to WHMs. Main difference is that a priest is by no means helpless, as opposed to a WHM who can't do anything offensively. Priests have nice shadow nukes, though i haven't played priest enough to accurately portay them. So again, feel free to correct my mistakes.
Mage is close enough to BLM to call them a parallel of each other, both focus on doing lots of damage in a short amount of time. Mages have much more crowd control and effective status changing spells than BLM.
Both warlocks and mages can move people. Warlocks summon others to them, mages send people away from them.
hope that helped a bit