What is the difference between an "autocomplete" and an "autocomplete (Tags style)" widget. These options are present when I add an entity reference field for example.
For one term, there is no difference.
When you increase cardinality (i.e. allow unlimited number of values), with tag style you will put all tags in one textbox, just like you do with tags on this site, and with regular autocomplete you will need to put each one with it's own textbox.