Are electric stove/burner elements/coils interchangeable
The answer is yes and no. Some brands have unique connectors but many are generic.  I would verify the wattage is the same and the fit is the same as long as those items are the same there should be no issues.
The connector issue could be a cheap one was used not high temp. When I repair stove wiring I use 900f degree connectors the standard ones you would get at a big box store are usually only rated for 90c max some only 75c these get loose with heat and start arcing until no contact area is left.