The difference is between broad consensus and divided opinion. A Constitutional amendment requires a 2/3 vote of Congress to propose, and ratification by 3/4 of states (which means any Constitutional amendment would require support from both red and blue states). Ordinary legislation only requires a 50% + 1 majority.

Yea,that's like... The entire point of the constitution. This is like saying "what's the difference between changing a law or breaking and entering after asking your friend Jeb if it's ok".