Serhan, I would recommend teaming up with someone experienced with the sale and/or purchase of default properties. All the terms you are asking about relate to properties in default.
In California there are a few stages of the non-judicial foreclosure process. Here is a brief overview of the process which will help clarify the terminology you are seeing on some properties on the market and advertised online.
When an owner has a mortgage and stops making their mortgage payments they are what's known as being in default.
The lender/bank then notifies the owners that they have missed payments and if payment isn't received, the bank will move to foreclose. After 30 days, the bank will publicly record a document called a "Notice of Default".
Usually about 90 days later, the bank can record a "Notice of Trustee's Sale" at which point the bank has scheduled a date to sell the property at a public auction. If the owner still cannot bring their mortgage up to date with payments and fees prior to the Trustee's Sale (or if they cannot begin one of many ways to postpone the sale date) - the bank will take back the property -- the property then is commonly known as "Bank owned", "Foreclosure" or REO.
Once a property is foreclosed, the bank's will market the property with a real estate agent and/or put the property up on an auction site. It usually depends on the bank, the current condition of the property and/or properties fair market value currently and in the near future.
Properties advertised with the disclosures Notice of Default, Auction or Bank Owned tend to relate to what stage of the foreclosure process the owner is in. Typically Bank Owned and Auction properties are sold in as-is condition with little to no additional disclosures relating to past repairs/issues as once it's Bank Owned, the owner is a bank (or servicing company) and they've never lived in the property.
Many times a property with a Notice of Default may be sold in what's called a Short Sale. This only happens if the fair market value of the property is less than what the owner needs to payoff their mortgage. The owner will need to get their bank' or banks approval to accept a lower payoff amount than the actual balance. This has the potential to requiring additional time during the purchase process.
I also agree with Jes on consulting a tax consultant regarding any different fees or procedures as a foreign investor.
Brian Selem - #01056044
Los Angeles, CA 90049