Red: in the Pikmin series red Pikmin are the strongest regularly obtainable species with immunity to fire. This is transferred to Smash with reds having the second highest attack strength and having immunity to fire projectiles and even inflicting fire damage on enemies when attacking.
Yellow: In the Pikmin series yellow Pikmin are immune to electric shocks and can be thrown higher than other types, similarly in Smash they have a slightly altered throwing arc and resist and inflict electric damage.
Blue: In the Pikmin series blue Pikmin are able to walk through water and swim, likewise in Smash they are immune to and inflict water damage. They also have the best grab range of all Pikmin which may be a reference to their lifeguard ability in the first Pikmin game that never came back. For those unaware blues left idle near drowning Pikmin would rush in grab and throw them to safety in the original game, it’s a stretch but I can’t think of what else to pull from.
Purple: In the Pikmin series purple Pikmin are the true strongest Pikmin type complete with hefty weight which slows them down when running. In Smash the purples are also the slowest and heaviest of the bunch and when thrown they fly a much shorter distance and just bounce off the enemy instead of latching on. This is a trait that the Rock Pikmin would acquire in Pikmin 3.
White: In the Pikmin series white Pikmin are the fastest and lightest Pikmin and have poisonous abilities, they are immune to poison and poison enemies when eaten. In Smash they too are the fastest Pikmin and are thrown farther, they also inflict darkness effect as Smash does not have a poison effect, they are not immune to darkness effects however.