Mortgages

The mortgage
In all but a few states, a mortgage creates a lien on the title to the mortgaged property. Foreclosure of that lien almost always requires a judicial proceeding declaring the debt to be due and in default and ordering a sale of the property to pay the debt.

The deed of trust
The deed of trust is a deed by the borrower to a trustee for the purposes of securing a debt. In most states, it also merely creates a lien on the title and not a title transfer, regardless of its terms. It differs from a mortgage in that, in many states, it can be foreclosed by a non-judicial sale held by the trustee. It is also possible to foreclose them through a judicial proceeding.

Most "mortgages" in California are actually deeds of trust. The effective difference is that the foreclosure process can be much faster for a deed of trust than for a mortgage, on the order of 3 months rather than a year. Because the foreclosure does not require actions by the court the transaction costs can be quite a bit less.