To add just a small amount of physics to MattPutnam's answer:
A guitar string is relatively simple to understand, because assuming that both ends of the string are fixed is a very good approximation - though it is not completely correct, since in an acoustic guitar the bridge must have some movement to transfer the vibrations from the string to the body of the instrument. That is one reason why guitars need to be "set up" to get the best intonation - the position of the frets can't be calculated "exactly" from the distance between the bridge and nut.
In high school physics courses it is often taught that the open end of a pipe corresponds to the free end of a vibrating string, and the closed end to the fixed end of a string.
That is over-simplified for the open end. When doing the simplest experiments on the resonance of a pipe, you have to apply an "end correction" by assuming the open end is actually a bit longer (in proportion to its diameter) than its measured length, but that simple "end correction formula" is itself only an approximation to the real behaviour.
To get close to the simple notion of the "open end" of a pipe, the pipe has to end in a bell or flare, like a trumpet or trombone, but that brings in different mathematical complications because the diameter of the pipe is no longer constant.
At a simple level, a flute can be considered as a pipe "open at both ends" but in fact the blowing hole affects the pitch in a similar way to the finger holes - and the size of the effect depends on the geometry of the complete system of the flute plus the player, not just on the flute!
The finger holes are not all the same diameter (as is shown in the OP's photo) and there is a tradeoff between the size of the hole and its position along the length of the pipe. It should be clear that the holes are spaced more or less evenly along the length, which is very different from the fret positions for the first octave along a guitar string.
It is easy to demonstrate the effect of the finger hole size on simple flute-like instruments (e.g. penny whistle, recorder, or even a baroque keyless flute) by playing a note while bringing a finger close to a finger-hole but not actually touching the flute.
The closer the finger, the lower the pitch. In fact this was a standard playing technique for "pitch bending" notes in baroque flute music.
Take home message: the acoustics of pipes are more complicated than they might seem at first sight - and they are much more complicated than stretched strings!