The attached diagram might help. The key difference is in how each type changes the voltage between the input and the output. The linear type of regulator passes the current through a variable resistor, causing a voltage drop to occur thus making the output voltage lower than the input voltage. The voltage control circuit compares the output voltage to a fixed voltage reference and then varies the value of resistance automatically to minimize the difference between output voltage and reference voltage. In this way the output voltage remains at a specific value regardless of how much current is passing through the variable resistance.
A switching regulator does not use this series resistor to drop voltage. Instead, it uses a switch that is turned on and off at a high frequency. Current that passes through the switch is then smoothed by a low pass filter, which also smooths the voltage. A voltage control circuit compares the output voltage to a fixed voltage reference and then varies the on-off-on-off duty cycle of the switch to minimize the difference between the output voltage and the reference voltage.
The essential difference between these two types lies in its efficiency. Since the linear type uses a resistor to cause a voltage drop, power is used up in heating up the resistor. In theory, the switching type uses no resistance and so has the potential of being 100% efficient. The tradeoff may be obvious in that the switching type is more complex. The switching type also generates switching noise in the output, the amount of which depends on the quality of the low pass filter.
One other thing worth mentioning. Since the switching regulator actually generates AC internally, you can design the low pass filter with reactive components to actually boost the voltage at the expense of current, a sort of transformer action. So it can boost your input voltage to a higher output voltage. The linear regulator can't do that.