What is a "chase" or "variant" rarity?

On NeonMob, there are five standard rarities: common, uncommon, rare, very rare, and extremely rare.  There also exist several other types of rarities.

 

A "chase" is a special type of rarity.  It may be extremely limited or different somehow from the main cards in the series.  It is represented by this rarity symbol:

A "variant" is a special type of rarity that typically indicates the card is a variation of a standard rarity card. In the example below, you can see "Cooz" and its variant "Cooz [Sketch]"