A lot of things which seem to be continuous aren't really.
Two points in the process of watching movies are actually discrete processes.For the first, photographic movies clattering through the projectors are discrete images sampled 24 times per second.
It's always been acknowledged that it's due to the "persistence of vision" that we run them together to perceive continuous movement, as we perceive movements that are continuous around us in wherever the real world is.
But it turns out that the mechanism which gives us the effect of persistence of vision is actually a process of discrete stages; thus, when we see continuous, real-world things, we perceive them in a sort of sampled manner.
Light energy (photons) entering the eye strikes a molecule of the chemical rhodopsin, the energy breaks a bond, & the molecule changes its shape. When the shape changes, it then releases the protein opsin, which then goes banging around in the neurochemical chain of events (mostly dependent on the *shape* of a molecule, like gears & woodruff keys) which make up vision. The rhodopsin somewhat slowly returns to its original configuration, & that period of slow return is where you get the persistence.
You see that it is discrete: either the molecule is in state A or B.
There's a lot of rhodopsin in our eyes, increasing the "population" of our "sample". We are acclimated to smear these samples together into our perception movement that we know is continuous, and that's why as frame rates go up, things get closer to our visual "sampling" rate.
I think you mean by your reference to analog events things like people walking, grass swaying, needles reproducing audio in grooves of records, which are continuous, & can be sampled to any rate to get whatever rate is needed for Your Particular Sampling Needs.
There are other photochemical receptors in the eye, they tend to have the same mechanism; rhodopsin is the dim light, monochromatic, baseline one. At some point, it seems like everything comes down to mechanisms that don't look or work too different from the transmission in a 1971 Triumph GT6.