When there are visuals I find them to be more "organic" on mushrooms and more "sharp/electric" on LSD, but that’s very subjective/suggestible.
But there are "social" trips where there are no visuals, usually when in a group and experiencing the substance together, there I wouldn’t be able to tell LSD and Psylocybin apart.
The feeling of shared being part of a shared consciousness, the cosmic laughter and the fractal thoughts can be the same with both substances.
I'd say there is a psychedelic state of consciousness and many different substances (Psychedelics) will get you there, the experience will differ in nuances, but the general idea is the same. Keep in mind that in this state you are highly suggestible, so the environment will often do a lot more to shape the experience than the exact substance.
Having done both about a dozen times, this is not my experience or the experience that others have shared. Even a large dose of mushrooms only has subtle visual effects, while LSD makes the world look like a van Gogh painting.
But visuals as strong as you describe I had only when I tried 25C-NBOMe. But there the mind trip was only barely present and the body feel was rather uncomfortable.
Mushrooms in particular are hard to standardize a dosage of. Eat enough of some strong ones and things get plenty visual.