2-way design vs. 3-way design means ?

@OP the term 'way' refers to how the frequency range is split. For the most part this will equate to the number of drivers used in the design. In a classic three way speaker, the drivers will cover the bass, midrange and treble. In a two way, the drivers will cover the bass and midrange - one driver, and the treble - the second driver. However, there are variations. For example, some of the classic BBC designs were three ways where the frequency range involved the use of a midbass unit, tweeter and supertweeter. However - this still involved three drive units.

And then there was the Bose 901. No way. 

Up until recently, the best overall loudspeaker I have owned were a pair of Eclipse TD712z Mk Is. They use one very special driver in a very special enclosure. No crossover. Direct connection to the music. They are surprisingly good at moderate levels and lack only a small amount of high treble and deep bass. The imaging and soundstage are amazingly accurate—sometimes too much so. I owned five-way, four-way, three-way, and two-way speakers that only did one thing better than the TD712s. But my latest speaker is a three-way with four drivers. It is a very, very good three-way, the TAD Evolution One. It is better than any speaker I have owned and on par with many other configurations of loudspeaker.

My conclusion: The number of drivers and crossover design is less important than their execution in the speaker.

No highs, no lows - must be Bose.

And then there was the Bose 901. No way.