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I am doing electrical work in my own home. Primarily replacing old sockets and fixtures. Through the course of this work I am finding odd, but not unsafe, wiring paths. I want to document these paths so that I can develop a plan to improve them. I also want to document my own work to help the next guy who does work in my house.

What is the diagramming style or name for the plan that an electrician would use in a residential home in the US?

I want to know what this is called so that I can then tell myself, "I need to make a $TERM diagram". I can then acquire the right rulers, templates, and graph paper to make those diagrams.

The correct term is an Electrical Plan. I used Smart Draw when I remodeled my home. It's a great tool and there are several templates you can choose from to begin editing. Its pretty cheap to use.

tl;dr "Electrical Plan" or "Wiring Plan"

A wiring diagram or electrical schematic usually shows each connection using sometimes cryptic industry symbols and with no routing information. They may be too detailed for your purposes, and they wouldn't show how the cables run through the building.

Example:

An electrical plan or wiring plan would simply show how the cables run through the building and what each cable's specs are (14/3, 10/2, etc.), possibly along with device notes (outlets, switches, utility appliances, etc.), and without showing each individual connection. This may be what you're describing.

Example:

On the commercial side with call them "as-built"s or "redlines" I've never seen an equivalent when doing resi. One generally ropes houses in the easiest/fastest manner while maintaining electrical safety, code standard, and good workmanship. In practical terms it means the usually the most direct / shortest route between devices on a circuit, while maintaining a neat appearance or the wiring.
Typical house wiring is simple and straightforward enough that one doesn't need to mark EXACTLY how that particular run was routed.

I'm not a electrician in the US and I'm not sure if there is an official type of drawing for what you have described but I use these for the most part

This is a screenshot returned from a google search for "schematic"
https://www.google.ca/search?schematic

There are a set of standard drawings to identify all elements of a system clearly that are universal at least in North American. I have seen some slightly different versions of the symbols on schematics from China.

This is an example of one https://www.drbijli.com/know-it/know-your-home-electrical-system/

it's not the best schematic if ever seen but it gets the idea across. You wouldn't need to learn many of the symbols either because mostly you need switches, lights and recepticals.

Home wiring is generally not very specific as noted by @isherwood . My house even less specific as the local code requires nothing smaller than 12ga , so it was unnecessary to list any gage. Even 220 V lines to various points are unspecified. Possibly because I drew them myself ( long story). I just drew in many lines; after it was wired ,the electrician told me he never ran so much wire in a house. If one had very specific plans , one would not have the fun of turning off the breakers to find what circuit went where.