1. Most things people call Venn diagrams are not Venn diagrams.
Lots of them are actually Euler diagrams. A Venn diagram has to show all possible logical relationships between sets, even if they’re not things that exist; an Euler diagram doesn’t.
2. If you want some added explanation, here are more charts than promised in the headline.
Venn diagrams are (roughly) a very specific type of Euler diagram. For example, a Venn diagram has to show the overlap between two sets, even if there’s nothing in that overlap (shown by shading it in black, as above).
3. While a Euler diagram can just show that they don’t overlap:
Venn diagrams also have to show every part of every set overlapping with every other at some point, which makes them really messy compared to Euler diagrams.