Does resistance to a damage type prevent similarly named conditions from applying?

Question

Creatures with resistances take half the damage from an attack of the type it is resistant to. But what happens if a condition is applied? For example, if someone with poison resistance gets poisoned condition, without any actual damage.

Answer 1

Damage resistance does not interact with status conditions.

The rules for damage resistance state:

If a creature or an object has resistance to a damage type, damage of that type is halved against it. If a creature or an object has vulnerability to a damage type, damage of that type is doubled against it.

No mention of status effects. Status effect immunity is an entirely separate feature from damage resistance and immunity.

Poison can be especially confusing, as resistance to poison damage does not a priori offer immunity or advantage against the poison condition, but features which offer one often also offer the other.

Answer 2

There is no such thing as "similarly named conditions" comparing with damage types.

Here's the list of conditions (per PHB p.290):

• Blinded
• Charmed
• Deafened
• Frightened
• Grappled
• Incapacitated
• Invisible
• Paralyzed
• Petrified
• Poisoned
• Prone
• Restrained
• Stunned
• Unconscious

And here's the list of all damage types:

• Acid
• Bludgeoning
• Cold
• Fire
• Force
• Lightning
• Necrotic
• Piercing
• Poison
• Psychic
• Radiant
• Slashing
• Thunder

It seems that Poison is the only type of damage with a condition of the same name. Having the same name is probably a coincidence, not a design.

By default, neither resistance nor immunity to Poison damage affects Poisoned condition in any way. However, they are often mentioned together:

Quasit

Damage Immunities poison
Condition Immunities poisoned

Aura of purity

Each nonhostile creature in the aura (including you) can't become diseased, has resistance to poison damage, and has advantage on saving throws against effects that cause any of the following conditions: blinded, charmed, deafened, frightened, paralyzed, poisoned, and stunned.

Thus, if poison resistance is accompanied by the poisoned condition immunity, it is said explicitly. There is no secret rule "Resistance to poison damage gives you immunity to poisoned condition":

Beware of claims that a rule does something mentioned nowhere in that rule or elsewhere in the core books. There aren't secret rules. (source)