Sandwich-Posting

Because they're both sausage, in English, with a bit of room for perception.

Historically, not every sausage was in a casing. But every sausage was prepared and seasoned, with preservation being a, if not the main goal

While most sausages across the world will be cased, there's plenty of variants that aren't. Most of those variants tend to be from very rural foodways, where preservation was meant to be short term and flavor a higher priority.

Here in the states, a lot of "country sausages" are ground or minced meats with salt, herbs, and spices not meant for long term keeping because they originated with offcuts. You'd make a pile of pork that wasn't big enough to do anything with for sale or storage by itself, and mince it, throw in your flavorings and cook it the same day or within a week or so if you had an icebox.

Patties come from that background. The "casing" still exists, but it's not edible. It's wrappers, cloths, or other items to shape the lump of processed meat.