The terminology I've heard of is called "degree of relation" or "degree of relationship". This is basically the number of steps (people) you need to take to get from the first person to the second person.
Nolan Lawson has a cute Relatedness Calculator that shows both the genetic shared percentage and the degree of relatedness. e.g. it shows a Second Cousin share 3.125% with a Degree of relation: 6.
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Charli Skipper gives simple instructions on How to Calculate the 4th Degree of Relationship for legal reasons.