I thought about calling this post 'mid-term prep' but that brings back memories of school, and I didn't feel like going there.
In my thought process, medium term prep is for situations lasting from days to months. Of course, many medium term preps can spill over into both long and short term- especially regarding durable tools. This is the focus of the largest majority of people with 'prepper' tendencies (again, by my observation). Categories of medium term prep include many food items, fuel and equipment, anything involving firearms, and trade and barter goods.
There are many others with many different schools of thought on this subject, and I'm not entirely certain I need to reiterate every point. For one, it would take too long to cover every aspect (indeed, considering how many subjects there are to be covered it could very well be endless); for two there are as many disagreements as agreements on this subject to even attempt an omnibus article. The salient point I have to make is this- anything that requires fuel or upkeep, anything that can be saved or stashed away is medium term prep. MREs may last many years on the shelf, and one may have a full years supply of three squares a day, but without the ability to restock, they will run out. Ammunition is the same story- reloading can greatly increase the time limit of your ammunition, but powder, primers and bullets (cases, too, although on a much longer time scale) are commodities to be used, and the supply will eventually run out. The key, in my mind, to medium term prep is to make them last as long as possible.
There are many doomsday style situations in which we can envision our preps being used, from terrorist caused grid-down to nuclear war, economic collapse to civil war, earthquakes and winter storms. The priority of each prep should be balanced by the severity of need and the likelihood of occurrence. For example- while preps for civil or foreign war on our soil are, indeed, very important, the likelihood of a winter storm that disrupts power is far more likely, and I would balance my preps towards the latter until I felt comfortable with my situation, then deepen my preps to my lower-likelihood situations. A walled compound with a moat and drawbridge, but without a backup generator is a little ridiculous. See to the necessary items first, then see to their security.
One thing that ties medium and short term preps together is access. Medium term preps are, by their nature, mostly stationary. Few people have the wherewithal to carry months worth of food and water with them every day. While it would, ostensibly, be possible, it would mean that pretty much everywhere one ventured would be in a large camper; this would get ridiculously expensive in a short amount of time, using money that would be better spent on supplies. This means that at least a portion of short term prep is geared towards getting back to the place where the medium term supplies are stored, and re-evaluating the situation once that security is regained. Conversely, long term preps tie over into medium term as well. I won't cover my long term preps at this time, but much of it is centered around food supply- decreased access to fresh food is a hallmark of any service disruption. Preparations made for long term, redundant, renewable food supplies can play a key part in making your medium term preps far outlast the length of time you would be able to survive on them alone.
In this manner, medium term preps are a bridge. Things like generators and stored food are put away as a stop-gap, between the immediate emergency and either the restoration of services or the establishment of long term solutions. Medium term security solutions (which deserve their own post) are intended to protect you and your belongings in a period of unrest. They are the difference between ease and hardship, whether the storm to be weathered is of man or of nature. Short term preps are for emergency survival; medium term preps are for surviving after the emergency. As has been seen in the vicious storms in the Northeast over the last couple years, services are not guaranteed within hours of a storm; every hour, every day, that one can fend for themselves, without requiring input from emergency services, frees up those services to help the less prepared, and can help immensely to shorten the overall length of the catastrophe. In the event of a total failure, on the other hand, medium term preps will buy the time needed to fully establish a long-term survival plan. It is vital to have these preps in place- after all, every bandage in your First Aid kit, every fire extinguisher in your home canno carry you through a power outage or a food shortage.