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the master may cast a spell with a target of "You" on his familiar (as a touch range spell) instead of on himself.

A master and his familiar can share spells even if the spells normally do not affect creatures of the familiar’s type (magical beast).

Worded this way, it seems a lot more like they're linked and less like it refers to all spells out of nowhere.

You are equating how PC class granted creatures operate and that is not True. RAW is descriptive and rationalized with each class a mostly independent object. Four distinct names ≡ 4 different things. There are similarities.

GMs have been executing the classes in play for 15+ years without issues (as PF1 is an OGL 3.5 spinoff). So it seems well understood.

It's not the classes being equated, it's a specific ability that is exactly the same for all.

The only differences are the types of creature they ignore (obviously), the two missing statements in the familiar, and a minor difference in the animal companion's Share Spells made to include multiclassed druid/ranger or other relevant combinations.
Which makes the omission in the familiar seem more of an error, because a sorcerer with the arcane bloodline (speaking of Core Rulebook, not later books that might have muddled up things as time went on) can also get a familiar, and might multiclass into wizard as much as druids and rangers can into each other.

Anyway, seems like the general consensus is that the 2nd statement is suborditate to the 1st, but then what was the point of it?
As other mentioned, in Core (and it seems in most other books as well) there doesn't seem to be any spell that both has "target: you" and is restricted by type (which also makes sense, unless we're talking about specific magic that certain types of creatures developed to use only for themselves, but that's not the case for most spells in all the books).