does the tuning advisor use the same engine/algorithm as estimated exec plan's recommendation?

Hi we run 2019 std. I learned a little about the tuning advisor with Olaf's help at https://social.msdn.microsoft.com/Forums/en-US/61b1d6c4-4df0-4dd2-bf46-646dc31a7f2c/can-the-tuning-advisor-make-recommendations-on-specific-queries?forum=sqldatabaseengine  .  Now I've become curious and more importantly interested in relying on the right tools in each situation.

does the tuning advisor (ta) use the same engine/algorithm as whatever generates estimated exec plan recommendations above the estimated plan graphic?  is the ta more advanced?  maybe the est plan's recommendation is more advanced?

I got 0 recommendations from ta on the original query discussed over at the other link.  But one index recommendation on the same query in the est plan's recommendation above the graphic.