Fresh sausage is a meat or meats ground with seasonings and occasionally other things and stuffed into a casing.
The differences are:
types of casing
types or combination of types of meats
seasonings
For example, at the outset, brats and Italian sausages are very similar. Then the seasonings are added and they become two different things.
Here's an ingredient list for Brats:
2 pounds Lean pork butt, cubed
1 1/2 pound Veal, cubed
1/2 pound Pork fat, cubed
1/4 teaspoon Ground allspice
1/2 teaspoon Crushed caraway seeds
1/2 teaspoon Dried marjoram
1 tablespoon Ground cayenne pepper
1 tablespoon Freshly ground white pepper
1 tablespoon Salt, or to taste
...and one for Italian Sausage:
2 1/4 lbs. pork
3/4 lb. pork fat
1 tbsp. salt
1 tsp. black pepper
1 tsp. fennel
2 cloves garlic, minced
1/4 tsp. ground bay leaf
1/4 tsp. thyme
1/4 tsp. ground coriander
1/4 c. cold water
Dried or cured sausages are another topic.