A teapot is designed for steeping and serving tea, with a spout for pouring and a lid to keep heat in. A kettle is used only to boil water — you pour the hot water from the kettle into the teapot, not directly into cups. A tea infuser is a small perforated container that holds loose tea leaves inside a cup or pot; it is much smaller than a teapot. In casual speech, 'pot' can refer to a teapot ('make a pot of tea'), but outside the tea context, 'pot' means a general cooking vessel.
The word 'teapot' is a compound of 'tea' (from Min Nan Chinese 'tê', via Dutch 'thee', entering English in the mid-1600s) and 'pot' (from Old English 'pott', related to Latin 'potus' meaning a drinking vessel). The word appeared around the 1610s–1620s, as tea drinking became fashionable in England and a dedicated vessel was needed for brewing and serving it.