Grenade

A grenade is an object thrown as a grenade-like missile as described starting on DMG 64. It includes boulders, containers of acid, holy/unholy water, oil, and poison.

Splash

Note that 3' splash is a radius, whereas listed AoEs are a diameter.1) Readers who miss this may be confused as to the listed oil AoE of 3' and wonder why it is the same as the splash radius (it isn't).

All creatures in the splash radius must save vs poison regardless of the grenade, not just for poison.2)

Poison splash

Poison is listed as having 1' diameter AoE, but all grenades splash within 3' radius (if they have splash listed). Readers might wonder how this is resolved, since there is no reduction in effect of the poison from being splashed. Why not just say 6' diameter AoE? The answer is because if a creature is in the AoE, they will need to save vs poison (assuming contact poison). But if a creature is only in the splash radius, they need to save vs poison to avoid being splashed, and any creature who fails that save must then save again vs poison for the actual poison effect. Being in the splash radius gives two saves, while being in the AoE gives only one.

1)
DMG 64, “All creatures within three feet of the impact…”
2)
Save vs poison is just the type of save used, it's not directly tied to the case of poison. This might be confusing since this rule is listed right after “Poison special”, but since the section is not listed as “Poison Splash Hits”, and because there is extensive precedent for use of saves not directly related to the name of the save, this is a reasonable ruling.