Is this the highest price ever paid for an LP?

Before the days of the internet, Goldmine listed the original test press of the 1st Bob Dylan album. There were six extra tracks that never surfaced to this day. It went for over $600,000. I'd be surprised if the Velvet Underground approached that.

What is the difference between an acetate and a test pressing?

Test pressings are made normally (stamped vinyl) to test the stamper for flaws I guess -- and generally given to various executives, etc.

Acetates are made before even a wax master is made. They are acetate-coated metal discs which are cut with a lathe (from the studio tapes) just like a wax master -- except they can actually be played (just a few times, because they're very soft), and are usually given to the artist for review/approval.
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According to an AP report, it was bought for 75 cents four years ago at a Manhattan flea market. Final eBay price was $155,401. [Not to shabby!] There is only one other acetate known in existence.