I have a square wave inverter, as you can see in following pic when i test live wire in square wave inverter, both output wires appeared as live wire but my pure sine UPS have only one live wire, why?
I can't vouch for any specific design, but one way to make an effectively negative pulse on a pair of wires that are supposed to be isolated is to put a positive pulse on the reference wire. ("neutral")
That's okay because they're both supposed to be isolated anyway and it's the ground pin that provides the safety function, NOT the neutral. (Ever noticed that the safety regulators require things to be either explicitly grounded or double-insulated? This is partly why.) Depending on other factors, that may or may not simplify the internal circuit.
A different design may have enough internal supply to make a negative pulse directly, or may use a transformer to convert a bridged(*) power amp into a single-ended signal.
(*) Bridged means two amplifiers that are fed the same signal but produce opposite outputs. Connecting a load between these amps, instead of between one amp and ground, produces twice the total voltage that would otherwise be available. This allows more output for the same supply voltage, or a lower supply voltage for the same output.
In the absence of any details in your question the likely scenario is as follows.
Figure 1. UPS circuit.
Your UPS output will either have a neutral connection straight through or, if the output is completely isolated from the mains, will have an earth connection to one of the output terminals. Either way, one of the wires will be "neutralised" and its voltage with respect to earth will be zero (or very close).
When you use a phase tester you connect the wire being tested to earth through the series circuit of the phase tester's neon bulb, series resistor and your body's capacitance to earth. Current will flow and the neon will glow when the circuit is live. On the neutral wire no current will flow as there is no voltage difference.
Figure 2. Inverter configuration.
Your inverter is most likely powered by a battery and has no earth connections on either input or output. There is, however, some stray capacitance between the output and earth and since the output is likely to be symmetrical the capacitance may be considered as lumped mid-way between the two output terminals. The effect is that when testing with a high-impedance measurement device such as a phase-tester both outputs will appear live.
Connecting something like a filament lamp to either output would effectively ground that output and the lamp would not glow. Connecting a lamp from each phase to ground would cause both lamps to glow dimly as both phases get pulled to ground equally.
If you wish you can probably neutralise one of the outputs but you would need to figure out the internals or check the schematic first to avoid damage. Again, the lamp test would show if there is a strong earth connection and, if that looks OK, then connect one phase to earth through a fuse. If the fuse doesn't blow then a solid connection should be fine.