what differentiates in 2/12 way and 3 way speaker ?

3 way = separate driver (or set of drivers) for treble, mid, and bass.
2.5 way = separate driver for treble, another driver that handles mid and bass, and separate driver for bass.

The simple differences are the 3-way separates the frequencies into separate drivers. and the 2.5 way gives you two drivers to deliver the bass.

3 way has a woofer mid woofer and tweeter, 3 way crossover.

Yes mostly, but it is a 3 way crossover design driving at least 3 drivers. It could have any number of drivers and still be a 3 way loudspeaker. A one-half way loudspeaker is when there are two (or more) drivers that operate in the same frequency range at some portions of the band but are cut off at different frequencies. It's a fine point though because it would still have a 3 way crossover. 

The 2 1/2 way is missing a high pass filter on what would normally be the midrange.

That’s the missing 1/2 component.

The advantages of 2 1/2 way speakers is usually having a small footprint but increased sensitivity, with some tradeoffs often occurring in the impedance being lower than it might be with a 3 way.

I’ve posted a thread here before that for many people the 2 1/2 way speaker may be ideal. Small, high output, deep bass.

Thank's Jeryg123 and erick_squires, very interesting