Let me clarify the states of a distressed home. I'm going to be very brief so I'll leave out the finer details.
1) The Home Owner is behind on their payments to their Mortgage Company this is the pre-foreclosure. The Home Owner can bring this current and the home will be removed from pre-foreclosure state. The amount reported prior to bringing current is the mortgage payments, plus late fees, penalties, etc. Not what is owed on the home. The amount late may be a small as one payment, or simply a property tax. The House may not even be on the market for sale and the home owner may not be interested in selling
2) Short Sale. This is where the home owner owes more to their lender than what a buyer will pay. It most likely will be on the Real Estate Multiple Listing Service (MLS) listed for sale. The amount listed is a starting point. The Home Owner's Lender will determine what they are willing to let it be sold for. If the market of similar homes are selling for less a buyer can offer less and the agents will need to "sell" the home owners lender on the value. If the house is listed under market value and the Seller's lender is aware of this, they are going to want more money than the offer submitted. A short sale can take 2 to 6 months for approval.
3) Foreclosure is when the Home Owner's lender has taken the property back. The house will be sold at the public auction for cash. The buyer assumes any and all issues with the home, other liens, title issues, repairs. This is not for an uneducated buyer.
4) As a person you can always write an offer on any home you want. Regardless if it is on the market or not. I recommend you have an agent represent you as a Buyer agent. The Home Owner doesn't have to accept your offer or they may. It's up to you.
Have an amazing day!