Hi,
The similarity:
- Both fields display terms to users to select.
The difference:
The only difference is how they store selected terms in the database:
- taxonomy
: doesn't store any terms in the post meta. Instead, it sets post terms. Think about it like a replacement of "Category" or "Tag" meta box of WordPress.
- taxonomy_advanced
: store terms' IDs in the post meta and doesn't set post terms.
Hope it's clear.