"And where do sherrif auctions fit in? I know that banks often buy the house......because they own the loan....but I'm not sure why or when a house ends up at a sherrif's auction when they would have gotten it when it went into foreclosure?

The "sherrif's auction" IS the foreclosure sale.

The property is auctioned according to the terms of the note.
Some places actually have the sheriff do the auction, other places that used 'deeds of trust' are auctioned by the trustee upon notice by the owner of the note that the terms have not been met.

The bank will bud at the foreclosure auction up to at least the value of the note (with any costs incurred possibly added).

If the bank wins the auction they now own the house, and it is commonly referred to as Real Estate Owned (REO).

The banks do not like the maintenance and other costs of ownership, but prefer not to lose money.

Mortgage insurance may have gone to the note owner if it is payable subsequent to the foreclosure.

If the bank does own the note, they may be willing to take the insurance and sell the house at more of a discount since part of the debt will have been paid.

Like many things in RE, how the banks handle things is local.

Oh. So the complete sequence is for sale, for sale short sale, sheriff's auction, foreclosure/bank owned?

So something that is for sale/possible short sale may not end up in foreclosure because it could be sold to a third party at the sheriff's auction?

Outside of sheriff sales for back real estate taxes or judgments, the sheriff's sale IS a foreclosure sale.

Foreclosure is what the note holder does when the terms of the note are not meant.

They way they accomplish the foreclosure is by a sheriff's sale or public auction, or even court action depending on the terms (and type) of note.

A short sale is when the note holder agrees to accept less than the value of the note (amount still owed) for releasing the note (declaring it paid off).

If the note holder would prefer this in some cases to a foreclosure, but not always.
It depends on how much of a loss the short sale is going to hit the note holder for.

Mortgage insurance may not pay the note holder when a short sale occurs, but is nearly always payable on a foreclosure.

The relative value of the propoerty, the note, any mortsage insurance, even the health of the note holder, can all come into play when the note holder must decide what path they wish to pursue.

In some cases their is also the possibility of a 'deficiency judgment' being recorded against the owner after the note holder sues them.
This can be mechanism to seize other assets the owner has that are not involved in the foreclosure.
Some state allow it, some do not.