My guess would be the v=XXXX bit is the actual video reference number which sites use for embedding, whilst the other is just a short link for easy sharing on social media which is converted to the full link by YouTube when someone accesses it. The "Share" link URLs provided by YouTube for other sites all have the full video link in them.
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When the YouTube site itself gives you this link: http://youtube.com/4jlkKdEjIio