Are these the same thing ?
Short answer: no.
'Curd' is the generic name for the solids obtained from coagulating milk.
Cottage cheese is a type of curd cheese that is unpressed, and not entirely removed of whey, so it stays creamy and wet, with soft lumps
Chhena is a curd cheese that is strained to (almost) completely remove the whey, and gently pressed to firm it up and form a more coherent mass of curd
There is no way you could call indian chhena a curd.
Recipes (taken from my mom):
Curd: Take lukewarm milk and add curd. Cover with a lid (most important step). Wait for 4-5 hrs.
Chhena: Heat 1/2 L milk and keep the flame on. Squeeze 1 full lemon in it. Keep stirring until the white part is completely separated from near transparent liquid. Filter!