What's the difference between observing in a given direction and operating in that same direction?

So starting with an up particle:
$$
lvert uparrow rangle = begin{bmatrix}
1
0
end{bmatrix}
$$
My understanding is that you can measure $lvert uparrow rangle$ in $X$ and have a 50% chance of getting $lvert leftarrow rangle$ and a 50% chance of getting $lvert rightarrow rangle$ where:
$$
lvert rightarrow rangle = begin{bmatrix}
frac{1}{sqrt{2}}
frac{1}{sqrt{2}}
end{bmatrix}
text{ and }
lvert leftarrow rangle = begin{bmatrix}
frac{1}{sqrt{2}}
frac{-1}{sqrt{2}}
end{bmatrix}
$$
but you could also operate in $X$ which would be the equivalent of passing it though a NOT gate:
$$
X cdot lvert uparrow rangle =
begin{bmatrix}
0 & 1
1 & 0
end{bmatrix}
cdot
begin{bmatrix}
1
0
end{bmatrix} = begin{bmatrix}
0
1
end{bmatrix} = lvert downarrow rangle
$$

I’ve read that measuring qubit spin is more or less equivalent to measuring the orientation of a photon which can be done by passing it through polarized filters. If the photon is measured to be in one orientation and then is measured in a different orientation it has a certain probability of snapping to be in that other direction.

So in this example, that would be equivalent to measuring an up qubit in $X$. But how does operating in $X$ come into the equation? I understand the mathematical effect it has, but what does this mean for the physical qubit? Is it also being passed through a filter and how is that different from measuring?

Thanks!