Not even close!

Baking Soda is safe for human consumption--It's Sodium Bicarbonate and was in use as an antacid for decades. It's used in toothpaste as well. You can even cook with it.

Washing soda is a DEADLY POISON, also called Soda Ash. It's Sodium Carbonate, not BIcarbonate, and gives laundry that really fresh, clean smell.

They are chemically different. One is safe for human consumption, which is why "baking" is in the title, one is not, which is why "washing" is in the title.