That is exactly right.
And you can also tell a similar story for the position-velocity relationship: if you make a wave by throwing a rock into a pond the resulting wave front will be circular, i.e. the position of origin of the wave is well defined (it's where the rock landed), but its direction of travel is not.
By way of contrast, if you want to make a wave with a well-defined direction of travel, the only way to do it is to make a very wide wavefront, i.e. one whose position is not well determined.
For example, placing a diagonal polarizer between a horizontal and vertical polarizer will allow light to pass through [3]. As you use more and more polarizers that gradually transition from horizontal to vertical, you converge on a mechanism for rotating horizontally polarized photons into vertically polarized photons without loss.
1: https://en.wikipedia.org/wiki/Quantum_Zeno_effect
2: http://algorithmicassertions.com/quantum/2015/10/26/Quantum-...
Is this just an apt analogy or is it basically the same concept at work in QM?
I do electrical engineering, and as far as I know, the uncertainty principle means that as the signal in the time domain gets more localized, the signal in the frequency domain gets more spread out (and vica versa). I think ( I don't know for sure) position can be thought of as time domain and momentum can be thought of as frequency domain (or it might be the other way around).
I'm not sure if this relationship actually leads to the Futurama "No fair, you changed the outcome by observing it!"
I could research this to find an answer, but it would take me way too long.