Pâté a French term whose meaning and use have both enlarged since early medieval times. The original meaning is best conveyed in English by the word pie (or perhaps pasty where the connection is more obvious). What was meant was a pastry case (a pâte) or coffin filled with any of various mixtures (meat, fish, vegetables), baked in the oven and served either hot or cold.
By a natural extension, the term came to mean not only the whole ‘pie’ but also what was in the pie. A pâté might be served in pastry, when it was a pâté en croûte, or without pastry but wrapped in bacon and baked in a terrine when it was a pâté en terrine (and here, by metonymy, the container, terrine, is now used to describe the contents).