Generally it's things that have been prepared such that there's some sort of added preservative -- salt, sulfates, sulfides, nitrates, etc. So this would include all hams except 'fresh ham', almost all deli meats, all sausages, bacon, jerky, corned beef, etc.
So yes, sausage is considered a processed meat.
If you want to get all technical about what 'processed' means it could also include any other form of curing (eg, smoking), and most any form of processing (grinding, slicing, etc), although this second group typically isn't refered to as 'processed meat' (unless it's then glued back together, like chicken nuggets, but those tend to have additives in them already)
As for the health aspects ... like most anything, it's fine in moderation, although there are some people who react badly to sulfates and sulfides. Some sausages have more additives in them than others, and there are plenty of sausages out there that might be considered 'healthy' if it's in place of other higher salt/fat foods (eg, some brands of chicken & apple sausage).
Any kind of cooked meat or fish and most perishable foods in general are safe as long as they are fully cooked and refrigerated within 2 hours (although the quality will deteriorate rapidly with fish).
If you plan to eat the leftovers twice then refrigerate two individual portions. Reheating the same item multiple times raises the risk of bacterial contamination. That is really the only thing you need to concern yourself with for short-term storage.
For more information see the USDA Basics for Handling Food Safely.
Best Answer
Check this essay: Time-dependent depletion of nitrite in pork/beef and chicken meat products and its effect on nitrite intake estimation
Check the Figure.1, while preserving meat in long days, the nitrite content in chicken sausage is much higher than pork/beef sausage.
For food safety, Nitrosamine where is transformed from nitrite is an important cancer factor. So there are only pork/beef(red meat) sausage in market but not for turkey/fish(white meat).