>Cousin of Bakelite? or same stuff, different trade name?
Yes and no, they are both thermo set plastics (they 'cure once' when heated, rather than melting).
But, Bakelite is made from urea, Tenite is made from Cellulose (the stuff wood mostly consists of) (Early Tenite was in fact made from wood)
There were other celulose plastics early on, celulose can be dissolved, and resolidifued with certain solvants, but the resulting "plastics" turned out to be rather ill behaved (like being flammable, sometimes explosive, sometimes simply disintegrating over time). The Butrated Cellulose plastics are more well behaved.....
Some of the early screwdrivers with 'plastic' handles were made from some of the less well behaved cellulose plastics, and didn't work out so well.....
(Have I gotten us sufficiently off topic yet?)