Can anyone tell me what sort of apple tree this is. The photos are current and from Eureka, California. I want to prune it up this winter/spring.
You'll almost certainly need to find a local apple grower's association that offers an identification service. In normal times, when local folks want their apples identified, the BC Fruit Testers Association offers in-person identification, but they require people to bring in 5 fruits from the tree (to get a sense of colour & shape differences and similarities)
It did seem complicated. I tried to do it myself using a guide but I couldn’t figure it out. There were so many factors with terms I didn’t know! I wonder how much it matters as far as pruning. I looked for something like you suggested locally and didn’t find anything. It is quite rural here.
It probably doesn't matter too much with respect to pruning. @vitog or @sgbotsford might have pruning advice.
Unless you want a really tall tree or an espaliered dwarf tree, the best pruning method is the modified central leader. Detailed descriptions can be found on the Web. Pruning for this shape normally is started when the tree is only a few years old; so the pictured tree will have to be modified slowly over a period of years to avoid excessive watersprouts and suckers. Most of my fruit trees are trained to 4 to 6 main branches to keep them short enough for easy harvest and pruning.
Looks like my Baldwins. All the top whippy branches will fruit next year and come down with their weight, thin them next winter if needed. I would thin out the lower density to begin finding a structure inside. It grows like a Baldwin too.