Are British curd, Cottage Cheese, Indian Chena 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