How are they different? I have read a lot about this, but I still can't differentiate much between them.
The difference is very simple. A linear-polarized antenna is designed to concentrate RF energy in a narrow plane. Imagine a strong water hose with a nozzle that has a narrow slit in it. Water would stream out in a narrow plane. A circular-polarized antenna, on the other hand, is designed to emit energy in a conical pattern. Energy travels in a corkscrew out from the reader antenna, and the corkscrew becomes larger as the energy gets further from the antenna.
If you can control the orientation of tags, then you can use a dipole tag and align it horizontally or vertically, and do the same with the reader antenna. This will give you the most read range. If you cannot control tag orientation, you will need to use a circular-polarized antenna. This will ensure that some energy from the reader reaches the tag, regardless of how it is oriented.
—Mark Roberti, Founder and Editor, RFID Journal