Whats the difference between evade and invincibility?

there are enemies that can break invicibility so if you use invicibility it will be useless but if you use evade you won't get damaged and vice versa

Basically evade gets between by Sure Hit, Pierce Inv, and an NP that Ignores Def (think Lu Bu, Emyia archer etc) while Invincibility gets only ignored with pierce inv, and of course both are buffs and can be removed.

Another cool aspect of the difference between the two is that they can stack, and Invincibility takes priority.

I abuse this on Cu all the time. I give him the Volumen Hydrargyrum CE, which gives him 3 invincibles, then I pop protection of arrows which gives him 3 evades. Evades don't get used up until the invincibilities are gone. This gives me 6 free hits where he takes no damage and usually protection of arrows has cooled down by then and I can pop it again!

- Ignore Invincible doesn't pierce any kind of Def or damage reduce buff, it's only pierce Invincibility and Evade buff. Li Shuwen Ignore all kind of survivability buff except Atk down and Guts.

- Evade and Invincibility one turn buff can't be stacked, you'll know the reason behind it. You can stack Invincibility one turn with non-turn based Evade, Invincibility takes the highest priority to take all of the hits first.

EDITED : Evade one turn skill and non-turn based Invincibility is stackable. However, Evade one turn skill and non-turn based Invincibility is not working really well if it's used at the same time.
Evade one turn will be useless here and Invincibility takes all of the hits first. It's better to use the Evade one turn after non-turn based Invincibility buff is gone.

- Non-turn based Invincibility and Evade can be stacked, like OG Chu + Volumen and Marie Rider/Caster ( 3 turn Invincibility ) + Basking Under the Sunlight ( 3 turn Evade CEs, coming soon but it's still a pretty long time ).
That would be 3 hits Invincibility and 3 hits Evade, it also increase the survivability of that servants greatly. 6 hits of hard defense buff is gone after taking 6 hits ? Then use the skill invincible/Evade skill again, using the Invincibility or Evade skill is like you rotate a wheel. Usually used by Soloist and i'm one of these kind of guys.
With Atlas Academy MC, Marie or Chu Invincibility/Evasion buff can roughly take 12-15 hits. It can become more or less depending on the situations.
Not really recommended if the enemies have permanent ignore Invincible buff, especially if that kind of enemies is a boss type.

- like mentioned before, the skill icon is different LOL XD.

I hope this can help to ease your mind a bit, btw i've got this info accidentally because i'm doing tons of solos to make this possible.
Usually solo lover veterans know this kind of stuff, there are more tricks to write but it will cause a problem named longpost.