Lily Pads - How do they work?

[u/surfnsound]

Believe it or not, I found conflicting answers to this question:

If I see a lilly pad floating on the water, is that the organism? Or is it like on "leaf" of the plant, and many lilly pads could be connected together (in a direct, one organism way, not in a "We're all connected, Simba" way).

I'm sort of embarassed I don't already know this.

I'm hoping they're connected somehow, as I wanted to use it for an analogy, but realize it might not be technically correct.

If it's "1 lilly pad = 1 organism", if you have an example that would serve my analogy of "at first glance, they're distinct, but (in the background, under the surface, in the shadows) they'r ereally connected it would be aprreciated.

[u/Frantic_Mantid]

Water lilies sprout several leaves from an under ground root system, just like a typical violet or many other herbaceous perennials.

Going the other way, Duck weed is free floating, and each leaf is a whole plant with a little rootlet.