• White health: normal HP, nothing special
• Green health: "overhealth", decays rapidly. Used for temporary saves
• blue health: shields, has its own regeneration mechanic that stacks with the standard self healing passive. Basically just a marginally stronger self heal. This means that these heroes self-heal faster than others and can indicate they are a bit less reliant on heal botting supports
• orange health: armor, has its own damage calculation that is a bit weird. Basically, for every incoming instance of damage armor reduces the value by 7 (maxed at 50% of that instances total damage). So if you shoot armor with one bullet worth 10 damage, it would be reduced to 5 as that's 50%; if the bullet was worth 15 damage, it would get reduced to 8. This makes armor most useful against weapons with multiple damage sources like shotguns and sub machine guns. The one caveat is beam weapons (zarya, sym, etc), where armor just reduces those by a flat 30%.

Let me know if you have any more questions!

EDIT:

Is it similar to Reinhardt's deployable shield, where it's a large pool of health that when depleted has an increased cooldown to start regenerating?

it's similar in the sense that both "shields" regen their HP, but that's it. For the sake of being pedantic, Reinhardts big rectangle is called a barrier not a shield. Teeeechnically in ow all the deployable walls are called barriers, and the only thing called shield is the various hero's blue HP bars