And dinosaurs are reptiles, mammals and reptiles are amniotes [1], both amniotes and amphibians are tetrapods, tetrapods are actually fish[2], and there's no such thing as a fish[3]!

[1] https://en.m.wikipedia.org/wiki/Amniote

[2] https://en.m.wikipedia.org/wiki/Tetrapodomorpha

[3] https://en.m.wikipedia.org/wiki/No_Such_Thing_as_a_Fish

So we have more in common with all land animals than a fish has with any other fish?

No, plenty of fish are closely related. There is however a lot more diversity so the extreme cases are far more extreme.

I've read that we have more in common with fungi than plants.

I vaguely remebering reading (I think it was in The Selfish Gene) that we are more closely related to salmon than salmon are to sharks.

This is absolutely true, and to be expected from the fact that the inheritance splits like a tree. For one thing both we and salmon have bones, sharks only have cartilage.

But we're more closely related to sharks than either is to the jawless fishes like the hagfish. The hagfish are just plain weird.

Humans (and all tetrapods) are more closely related to lungfish and coelacanths than either of those two types of fish are to other living fish.

Is it that surprising? The land is populated only by the descendants of a few species that moved into it.