Electric Steam
This type was the first kind espresso machine that ever received any real popularity in the American mainstream. Here's how it works: water that has been poured into a reservoir is heated to boiling.  This same pressurized water is used both to steam milk and brew the espresso.  This method gets the water pressure up to about 1 bar (although, the preferred pressure at which espresso is brewed is about 8 bar). 

Many folks like using an electric steam espresso machine in order to brew a coffee just a bit stronger than drip coffee.  However, given the advent of the next type of machine, boiler machines are now of out of step with mainstream espresso connoisseurs.

Electric Piston
The electric piston type espresso machine, produced by companies such as La Pavoni, is very classy looking and can actually be a lot of fun to use.  Although some folks are so enamored by their aesthetic appeal that they put them up for shelf display, they are actually capable of producing a pressure of 8-9 bar, the benchmark pressure of a genuine espresso drink.  Like the steam boiler model, the water reservoir heats up to the appropriate temperature for both milk frothing and steaming. Just open the steam valve and let the foaming begin. 

The pressure for brewing espresso is achieved by pulling on a hand lever which is attached to a piston.  Pulling the piston up brings water into the group, and pushing it down forces hot water through the grounds in the portafilter.

• The user has precise control over pressure applied.

• Often a thermometer is included so that you know when your water is at optimal temperature.

• The porta-filter is usually heavy-duty, like the machine's hull. 

• Not just any ape can figure these out (this ape, for instance, needed a bit of time to learn how to operate one of these machines expertly).

• Some units can be quite loud during initial heating up.

• The reservoir is one big boiler, so the unit can often take quite some time to heat up (several minutes).

• Since steaming water is maintained in the boiler, the water may be considered by some to be too hot for brewing.

Pump
The pump machine has made things much easier for espresso lovers.  Electric steam machines didn't make enough crema, but electric piston machines could get a little unwieldy. 

The pump machine uses a pump that pulls water from a reservoir and returns it into a tank that heats the water.  Two separate thermostats control brew temperature and frothing temperature.  After the boiler heats the water to brewing temperature and the brew button is pressed, the pump activates and water gets pushed through the boiler, then through the grounds in the brew head. 

In order to froth milk, the steam button is pressed and the unit also heats the water in the boiler, but to a hotter temperature than brewing temperature.  Since brewing and steaming occur at different temperatures, sometimes multiple heating systems are used so that the user doesn't have to wait between brewing and steaming.  After steam is produced, a valve can be opened, releasing some of the steam through the wand.

The first pump machines operated with a boiler.  The boiler, however, can take up to ten minutes to heat up.  The next series of pump machines included a heating system which could heat the water in a matter of minutes. Today's pump machines usually take between fifty to ninety seconds to heat up, and many use super-fast heating systems called thermal blocks or thermal coils.  Others still use small boilers. 

Traditionalists and espresso "purists" prefer the quality of espresso produced by a boiler machine than that produced by a thermal coil or block.  However, for the average consumer, the difference in flavor is nearly undetectable.