If order has to be preserved, doesn't this require moving three?

In this solution, I'm seeing the horizontal of the "T" as the 1 from the initial setup.

But you still need to move the right side of one 0 out, and the bottom of the other up (to make the A). That first move could be to contribute to the T, but that still leaves the vertical part of the T at the beginning. What am I missing?

I'm not sure what "order" refers to here.

My understanding of the solution is that you view the initial setup from the left (effectively rotating the initial setup 90 degrees anticlockwise). Then 2 moves are required:

1. Move what is now the bottom of the middle square up to create an "A".
2. Move what is now the right of the top square to be the vertical of the "T", leaving behind a "C".

So the trick is that the "1" from the initial setup becomes the horizontal of the "T" without needing to move anything, simply by viewing from a different angle.

An alternative way of looking at it: 2 moves gives the word:

C
A
T

but rotated 90 degrees.

Having explained this, it's made me realise what you mean by "order". The "1" is the first character, but the "T" is the last character.

The reason the "T" doesn't require 2 moves despite changing from first to last is that the whole image has been rotated so the "1" goes from being first horizontally, to last vertically, so only one toothpick needs to be moved to convert it to a "T".

Oh, rotation! I get it now. I thought the answer was just showing each alteration in turn, but that orientation matters.

Showing it in the original orientation first, followed by the rotated version that is readable, might help future viewers.