If the output of the bridge has a capacitor filter then the DC output will be approximately 1.4 times the ACrms voltage minus the voltage drop through 2 of the bridge diodes at light load. It will drop as the load increases, depending upon the resistance of the transformer and the bridge diodes.
A switch-mode power supply rapidly switches the input power and uses an inductor or transformer to convert the input DC voltage to a different voltage (either higher or lower) with high efficiency (often higher than 90%).
A linear supply can only reduce a voltage and it does this by connecting a variable resistive element (typically a transistor) in series between the input voltage and the output load, wasting the dropped voltage in heat dissipation equal to the voltage drop times the output current. Its efficiency is generally low, being equal to the ratio of the output voltage divided by the input voltage.
An unregulated supply does not regulate the voltage for either input voltage variations or output load variations. A simple bridge rectifier and capacitor falls into that category.
A regulated supply uses electronic elements with feedback from the output to keep the output voltage (or current as desired) stable with changes in input voltage, output load, or other variables such as temperature. A regulated supply can be be either linear or switch-mode.