Answer by sepaugh · Jul 20, 2015 at 01:55 PM
In short, an inverter is the heart of a UPS. The inverter takes DC electricity from some source and generates AC electricity to power some device or appliance. An inverter is typically designed to run for a sustained period of time (usually constantly). A UPS is a special application of an inverter where the DC source is batteries and is typically designed to run for a short period of time (usually several minutes) which is just long enough for either the downstream equipment (like computer equipment) to be shut down properly or until an alternative AC power source can come online (like a generator). The length of time a UPS can run inversely depends upon the load current applied to it (more load equals less run time).
For more info:
Make an inverter : DIY Experiments https://youtu.be/VDi_uFSr3w0
Inverters (With a side bar on UPS at the bottom of the page) http://www.explainthatstuff.com/how-inverters-work.html
A Power Inverter FAQ (with questions regarding UPS differences) http://www.tripplite.com/support/inverter-faq
Interested in the science and math behind all of this? Here's lecture notes from MIT http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-334-power-electronics-spring-2007/lecture-notes/ch9.pdf
Hope this helps! Mitch