Ice Magic Status Effects

So, I've been learning and building a pure ice mage build and came across a few things that I'm not sure of. Some abilities have the description of activation after an enemy is frozen or frostbite. What exactly is the difference between frozen status and frostbite status? And is there any visual indicator that tells which is which?

From what I understand, frozen is when the enemy is slowed, and has a frosted visual, and the snowflake icon under their HP bar. Is frostbite different?