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The "time" has nothing to do with the tempo. Sure, that may make it a dumb word to use, but it is what it is.
8/4 time isn't necessarily faster than 3/4 time. It just says there are 8 beats before the composer is going to put another little vertical line on the staff. Measures really only exist as a reference to help musicians play together with each other, kind of like page numbers. You can transcribe music into a different time scale if you want to, just like you can transcribe into a different clef. Some time scales inherently suggest an accented beat, like 3/4 time is expected to have that familiar "DUN dun dun" waltz sound, but you could write that same waltz in 4/4 if you really wanted to, and just put egregious accent marks on every third note as necessary.
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