All professions have 1 of their 5 skill slots dedicated exclusively to a small selection of healing skills. Obviously, there are only so many ways to design a healing skill (heal immediately, or heal over time; heal single or AoE; skill is active or passive), so when designing 3 heal skills for each of the 8 professions, some overlap in the core mechanic (healing) is unavoidable.
However, they are not the same; every profession gets its uniquely flavored healing skills, tailored to their general abilities and allowing for various playstyles. A Necromancer's healing skill might involve draining an enemy, while an Engineer's healing turret also heals nearby allies while the turret is alive, or he dispenses bandage packs that can be picked up by any ally. A warrior's healing skill might provide passive regeneration and an active, immediate heal, while another trades the passive heal for an adrenaline boost when using the active, increasing your fighting power.
In essence, it's true that there are no dedicated healers - if any player just stands around and takes a lot of damage quickly, it will be pretty much impossible to save him with healing skills alone. Dodging, positioning, and selecting the right weapon/skill loadout for an encounter (i.e. skill and game knowledge) are much more relevant for survival than healing skills or gear quality.
Every player in Guild Wars 2 might have some abilities to heal or protect each other, which means that there is no holy trinity. No character will only tank (it will also heal and deal damage), no character will only deal (it will eventually need to drop some heals) and no character will only healbot (it will be dealing damage, and may even tank).
Besides that, all characters will be applying eventual boons to party, so as protection zones and overall support skills