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

A 2 way speaker has a bigger physical demand put upon the 2 drivers of a  tweeter/mid bass. Think about this...those 2 drivers have to make ALL the sounds!

The load is reduced when you divide the frequency and add a speaker to handle just the mid-range and a speaker for just the deep sub bass. The mid-base driver isn't jumping around as much trying to reproduce everything when the load has been greatly reduced by adding a dedicated mid-range and a sub-bass driver.

The same reason why a subwoofer is designed to handle ONLY the deep bass. With the addition of a high pass filter the mid-bass driver can breath easier and has much less movement to the cone surface. Less distortion is the goal.

4 way speaker... is a tweeter/midrange/midbass then add a subwoofer.  

Whether a design is two way or three way won't tell you a whole lot about its capabilities.  Some people even swear by a single driver design (although I have yet to hear any of the exotic examples of them).  As most audiophiles will tell you, listening to a speaker in YOUR room with YOUR components is the only true way to see if a speaker is to your liking.  There are subjective measurements like tonal accuracy and dispersion patterns, but only your ears will tell you what works well in your setup.  I personally love the three and four way designs by Tekton Design because the concentric tweeter arrangement handles different frequencies within the mid and upper mids.  I own the double impacts and impact monitors. 

Sound advice from jrareform. I’m old enough to have owned and sold all the driver perturbations. It’s not intuitive. For example my flagship model Voxativ single driver speakers were faster and more precise than Zu flagship 3 way model (with built in separate bass unit — so maybe 4 way). Audition them as best you can.

I thought it had to do with crossover design. ie  The crossover is cut into three sections and therefore you can feed the three individualized signals to as many drivers you want. This is a three-way I guess

To say how many drivers a speaker has doesn’t necessarily mean whether it’s a two-way three-way or four-way.

@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.