There are commonly 2 types of Oxygen Sensors found on engines, Narrow and Wideband. As the name suggests, a Wide band Oxygen sensor (O2 sensor) is capable of reading a wide range of fuel mixture ratios, typically reading from 8.0 - 22.0 parts of Oxygen to every 1 part of fuel, also called the 'Air Fuel Ratio'
Wideband Oxygen sensors are composed of ceramic, platinum and other precious metals and have a 'heater circuit' built into the sensor.
A Narrow band sensor usually reads from 14.0 - 15.0 parts of oxygen on a petrol engine and will produce between 0.1 and 0.9 volts. The sensor communicates to the Engine control unit (ECU) if the the mixture is rich or lean but not by how much it is off the stoichiometric ratio of 14.7:1 AFR.
A Wideband O2 sensor will typically produce from 0.1 - 4.9 volts giving a lot more resolution for the ECU to read how far rich or lean the fuel mixture is from the stoichiometric ratio of 14.7:1 AFR. This allows the ECU to trim the fuel mixture to the desired ratio set by the engine manufacture or engine tuner for optimum fuel efficiency, torque or safety measure when in 'closed loop mode'.
Lambda is another common term used to read the ratio of oxygen vs. fuel and is the oldest unit of measure. In a petrol engine the stoichiometric air to fuel ratio is 1.00 Lambda.