Bitcoin Proof of work puzzle inconsistency

Bitcoin Proof of work puzzle inconsistency

At this time, I am really confused about the Proof of work puzzle because as I have seen in some documents, there are 2 different ways to talk about them.

The first one I have seen is from some videos, and also the original of Bitcoin by Nakamoto: the answers to the puzzle will make the result of hashing the block header contains some number of zeros from the start consecutively.

Meanwhile, there are also some documents saying that the result of hashing the block header has to be below a difficulty.

So I wonder which one I can trust now. Could anybody tell me? Thanks in advance :-)

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