What Is The Difference Between Hotdog & Sausage?

This morning I was having breakfast in a "kopitiam" (a traditional coffee shop found in Southeast Asia) style western food restaurant and saw a breakfast set of "egg & hotdog" on the menu. It prompted to me that I have been wondering about the difference between "hotdog" and "sausage".

So browsing thru the internet and found below definition that are widely used.

Sausages
The high quality traditional German sausages first came from Neu-Isenburg, a small town on the road from Frankfurt to Darmstadt. It is made of prime lean pork and a little salted bacon fat. It is then finely chopped into a smooth paste, put into pork casings and smoked.

Hot dogs
The stuff that we call hot dogs are made from very different ingredients and most probably came from America. These ingredients can be anything like pigs' and cows' hearts; and pigs' cheeks. Iced water is added at around 1/3 the weight of the meat and stuffed into narrow bullock runners (casing) and smoked.

It seems that the main differences are:
(1) Place of origin;
(2) Ingredients.