We see following terms in different water purifiers. Here, I will try to explain meaning for them.
UV [Ultra Violet]
This kind of water purifier will be having UV lamp which destroys the bacteria in the water by powerful UV rays. The body of dead bacteria will still remain in the body if there are no filters after UV stage.
UF, Nano, RO
I have mentioned all the above terms in the same heading as they are related. They basically filter out smaller particles from water. In all the three technologies, water passes through membranes having very small holes. Particles which can not pass through membrane holes will be filtered and water gets purified. The holes in membranes are very very small which can even remove the dissolved particles and minerals from water [in case of RO].
UF [Ultra Filtration]
In this case, membranes are having holes in the range of 0.01 micron [0.01 micro meter or 10 nano meter]. To relate the size of the hole, you can consider thickness of human hair, which is around 100 um [100 micro meter (um) OR 10th part of millimeter (mm) OR 10000th part of centimeter (cm)] on average. So this membrane will be having holes which are 10000 [ten thousands] times smaller than human hair.
Nano
In this case, membranes are having holes in the range of 0.001 micron [0.001 micro meter or 1 nano meter (nm)]. It is in the range of 1 nano meter, so it is called Nano filter. So this membrane will be having holes which are 100000 [one lac] times smaller than human hair.
RO [Reverse Osmosis]
In this case, membranes are having holes in the range of 0.00001 micron [0.00001 micro meter or 0.01 nano meter]. So this membrane will be having holes which are 10000000 [1 crore] times smaller than human hair. Holes are so small that it even filters out minerals from water. This is why one should be very careful in choosing RO water purifier because it can filters out most of the useful minerals from water apart of other impurities.
If TDS in water is upto 500/1000, one can choose UV + UF or UV + Nano water purifier. This will make sure all impurities [But not minerals] will be filtered out through UF / Nano filter and bacteria will be destroyed through UV. If UF stage is kept after UV, it will also make sure that dead bodies of bacteria destroyed through UV will also be filtered out from water.