It's a kind of pitch instability: https://en.wikipedia.org/wiki/Wow_(recording)

Basically, on analog media, playback speed isn't perfect. There's constant speedups and slowdowns. This creates a "waa waa" or "wow wow" effect that's noticeable when playing a constant pure tone.

Similar to how the different film stocks affected the look of the image, the different tape formats would effect the sound similarly. Crudely explained, the more light brown the tape, the more noisy it would be. The darker the tape, the cleaner it could be. If you like the sound of someone standing behind you constantly saying shhhhhhhhhhhhhhhhhhhh, then choose a brown tape.

By now, the audiophiles have lots of profiles of what the various tape formats would sound like. It's been ages since I've looked at audio plugins, but I would be shocked if there's not presets to make your pristine audio sound like a Maxell cassette that's been played hundreds of times.

You might want to have a look at https://github.com/jatinchowdhury18/AnalogTapeModel

Available as a (free) DSP: https://chowdsp.com/products.html#tape