Baking soda is Sodium Bi Carbonate also called Sodium Hydrogen Carbonate
Washing soda is Sodium Carbonate without the Bi or Hydrogen
They are chemically similar. But, the Bi Carbonate will neutralize acids where the Carbonate just dilutes acids.
I have used Baking Soda to clean the burnt stuff off the stove top with great results.
The procedure I used was as follows.
Clean off all the easy to remove stuff.
Mist the surface with Hydrogen Peroxide. I use 3% from the grocery store.
Spread Baking Soda over the burnt on areas.
Re-mist to keep the area moist for an hour or more. This mixture eats through a layer of burnt on gick.
After an hour, or overnight, wipe off. A layer will be gone without any scrubbing.
Depending on how thick the original mess was you may need to repeat a few times.
This process isn't quick, but, it is really easy.
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