The terminology Nth cousin Mth removed is common, but I was wondering if there are other notions of "distance" on genealogies? For example looking at the Cousin tree (with genetic kinship) chart at the ISOGG Wiki, we see that both first cousin and grand-aunt share ~12.5% of the genome IBD with the individual labeled "self". They both are also 4 links away through their MRCAs. Is there a common notion of genealogical distance that captures this?
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.
Charli Skipper gives simple instructions on How to Calculate the 4th Degree of Relationship for legal reasons.
Gedmatch uses a number system for generational distance.
It's based on the DNA and often gives incorrect predictions of relationship. Not just wrong about which of several relationships it can be (of those with similar cM match ranges) but wrong about the GD directly. Especially for those of us from endogamous ethnic groups, the GD is often higher than it should be.
Still, it does describe relatedness and can be used in ways other than looking at the actual DNA.
In this system, a GD of 1 means a parent-child relationship. First cousins have a GD around 2. Why do I say "around?" Because it's measured to tenths of a unit and most relationships can vary by a few tenths.