What is the difference between a time of flight mass spectrometer and a spectrometer that uses a magnetic field?
Both types of mass spectrometers separate different chemical species based on the mass-to-charge ratio.

The time-of-flight mass spectrometer (TOF MS) is based on the ions being released at a given instant, such as when struck by a laser, accelerating the ions electrostatically and measuring how long it take for them to strike the cathode target. This is ideal for a lightweight interplanetary or cometary mission such as Rosetta. 

Magnetic and quadrupole MS work by bending the beam magnetically  or electrostatically so as to spread out the target beam along the width of the target. This is like sending a light-beam through a prism to spread out the spectrum. An advantage of this technique is that it can resolve multiple species simultaneously, but at the expense of fine resolution.

An excellent explanation of TOF and other MS is presented by Young, Waite and Miller.