Does the term "variants" refer to the .cpf and .cop fils?
Variants are (differently) rendered versions of a Raw file. Each Raw file can be rendered is different ways in Capture One. When you right-mouse-button click on a thumbnail (the current variant), you can choose to create a New Variant (a not yet edited version, beyond default rendering), or Clone a Variant (a copy including all the current edits). One could look at Variants as being snapshots or alternatives of the same Raw source image.
By making such a Variant, one can assign a different/new processing engine to a Variant, or keep the original engine's rendering. Variants can be Picked (made the primary choice), or Promoted/Demoted to change their order of appearance in the list of thumbnails, in the Image menu. This also allows to look at multiple variations of rendering the same Raw file side-by-side, and choose a prefered one.
This also allows to Proof and tweak different Variants for different output media/gamuts, but that can become difficult to track unless you also keep a record of it with added keywording (e.g. add an intended Output medium keyword hierarchy).
Cheers,
Bart