What is the difference? I have two GE preheat ballasts for 14,15,19 0r 20 watt lamps, tow starter sockets and the old ballast.
Reactor has only two terminals (as it is only a simple choke), it's only purpose is to regulate the lamp current by inserted "ballasting" impedance in series with the load (lamp arc). It is the simplest and most efficient form of the ballast and as such could be used, when the mains voltage is at least about twice the lamp voltage (230V for all lamps i know, 120V for some low wattage only - the F20T12 should fall in this category).
The autotransformer has three terminals - neutral (primary end of winding), line input (usually the tap between primary and secondary) and lamp output (the secondary winding end), while the leakage inductance between both sections is used as ballasting impedance. Beside of the current limiting function it increases the open-circuity voltage, to be roughly twice the lamp arc voltage. It is necessary, when the lamp arc voltage is more then about half of the mains, so simple choke could not be used (120V for all, except of low, wattages).