"He is over 50"

Here's one of the most significant differences:

403(b) contribution limits are $22,500 in 2023, and $23,000 in 2024. 403(b) catch-up contributions let those who are 50 and older save an extra $7,500 in 2023 and 2024. All of that is put into the 403(b). Don't be confused that the value $7,500 appears in different provisions. They don't link.