Is there any relation between the meanings of the word "cataract"?

Actually, this was fairly easy to research. From Wikipedia:

"Cataract" is derived from the Latin cataracta, meaning "waterfall", and from the Ancient Greek καταρράκτης (katarrhaktēs), "down-rushing",[52] from καταράσσω (katarassō) meaning "to dash down"[53] (from kata-, "down"; arassein, "to strike, dash").[54] As rapidly running water turns white, so the term may have been used metaphorically to describe the similar appearance of mature ocular opacities. In Latin, cataracta had the alternative meaning "portcullis"[55] and the name possibly passed through French to form the English meaning "eye disease" (early 15th century), on the notion of "obstruction".[56] Early Persian physicians called the term nazul-i-ah, or "descent of the water"—vulgarised into waterfall disease or cataract—believing such blindness to be caused by an outpouring of corrupt humour into the eye.[57]

https://en.wikipedia.org/wiki/Cataract

All of the above are true but, to fully answer the question, it's worth mentioning three more archaic usages of cataract:

1. to describe a deluge of rain (I wonder whether both waterfalls and extremely heavy rainfall - especially when cascading from a roof - can feel rather like a Roman portcullis, preventing travel either into or out of a building, or - for river travellers - an unexplored continent?);

2. similarly, to describe a waterspout or geyser - where turbulent swirling water shoots up from underground to drench onlookers (sometimes imagined at the mouths of caves and tunnel systems, these can act with the sudden, daunting unpredictability of an enemy portcullis - deterring venture);

3. lastly, to describe a tempest or whirlwind - especially where raincloud, but sometimes milky-white cloud, gets twisted up in the swirl. This last, ancient, usage is probably the imagery wrapped into Wordsworth's decidedly spiritual quote.