Hello, Joe,
first, good question!
In first instance, it's a matter of design - basic layout of the components, availlable space.....length of the
levers....almost everything of the basic geometry plays a role here.
The absolute number of columns isn't that different though - at least generally speaking. Of course it's obvious that the more columns, the smaller the angle of rotation for one increment (i.e. from one position to the next) - depending the levers and their
proportions this may translate into different pusher action/feel - or not. We would have to look at the whole picture always.
But, one interesting point in regards of the number of columns - sometimes you'll observe the same caliber with different numbers
of columns on the column wheel.
The sequence of the column wheel increments for a normal two pusher chronograph is simple: 0-1, stop - run (the reset is controlled seperately by the reset lever, without direct interaction of the column wheel, the column wheel only allows reset during
stop position)
That means, the increments are controlled by the ratchet wheel profile on the bottom part of the coloumn wheel, here's a picture:
The sequence of 0-1 means, the ratchet wheel teeth number to column number must have a 2:1 ratio. This results in an repeated 0-1 pattern when switching through the natural ratchet wheel increments.
Now, think of a one button chronograph, the sequence here should be 0-1-2, i.e. stop, run, reset - all controlled by the column wheel.
The ratchet wheel teeth number to column ratio here needs to be 3:1 - that's the way to have three different positions of the columns wheel as constantly repeated pattern/sequence.
Have a look at your first picture of the Minerva chronograph - that's a mono pusher obviously. As to have the 3:1 ratio this one has
only 5 columns , the ratchet wheel would have 15 teeth (=3:1). The two pusher variant of that caliber has 6 columns, and ratchet wheel teeth count is 12 - which results in a 2:1 ratio needed for the two pusher sequence.
Many chrono movements exist (or existed) in two versions - one and two pusher - you can determine the difference from the different
column wheel number than.
Hope above isn't too confusing and will clarify your question a bit.
Best regards
Suitbert