Bunions and hallux valgus are somewhat different things, but the terms are often used interchangeably.
Bunions are a medial bony and soft tissue (mostly bursa) enlargement of the big toe (hallux) joint.
Hallux valgus is a deviation of the toe in a valgus direction (to the outside of the foot).
From these two definitions, it can be seen how they mostly occur together, but the bunion is referring to the lump and the hallux valgus is referring to the deviation of the toe.
The term hallux abducto-valgus is more used by those who want to use a more precise terminology. Valgus is in generally considered as a frontal plane position, so the “valgus” here is referring the the rotation of the toe in the frontal plane. Abduction is a transverse plane motion, so the “abducto” refers to the abduction position of the hallux in the transverse plane (whereas the above definition of hallux valgus uses “valgus” to describe this transverse plane deviation).