They are not the same thing. Sausages are any kind of meat (or animal product) and spices in a casing. Weenies or wieners are a specific TYPE of sausage. They have a smooth texture, meaning that when cooked the outside skin is smooth rather than rough, and are typically made from a mixture of beef and pork. Wieners, hot dogs, and frankfurters are the same thing. Italian or breakfast sausage will have a rough texture when cooked, and are not called wieners. Other smooth-skinned sausages, such as liverwurst or blood sausages, are made from ingredients and spices that are different from wieners.
The slang meanings mentioned by the other posters are correct.