If I use T568B at the wall socket, does the other end need to be T568B as well?
For a normal straight-through Ethernet run, yes. If this end is terminated as T568B, use T568B at the far end as well; likewise for T568A.
Different runs can use different schemes, although a building full of mixed A and B terminations can become a small labyrinth to document for no real benefit.
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