That’s why I also put the top picture on there. That one is clearly Jensen and Jared, just hanging out on set. The second picture doesn’t look like Jensen’s face when he hugs Jared. It looks like Dean’s face when he hugs Sam. Much more serious and world-weary.
Here’s Jensen hugging Jared:


And here’s Dean hugging Sam:


That’s why I was guessing that this:

might be a brother hug.
Although yeah, if J2 are randomly hugging on the set, I need to know about it for scientific research purposes.