Yes, it's blanket weed since you can pick it up. Blanket weed is a very general term which can be applied to any macro algae.
The blanket weed treatments you used, whatever they were, would in general kill the blanket weed. That leaves you with dead blanket weed, which decomposes and breaks up when removed depending on how much decomposition has happened. Blanket weed treatments generally don't actually remove anything. If you wait long enough the blanket weed will decompose to the point you don't see it, at which time most people think it has disappeared. But it's all still there, laying on the bottom or dissolved in the water.
Blanket weed will also die and decompose on its own in a natural life cycle. Blanket weed treatments in a perfect world are used to stop blanket weed growing, killing it as it sprouts. But most people wait until they have a blanket weed problem, apply the treatment, and end up with a bigger problem. BTW, most blanket weed treatments are toxic to fish despite what the front of the bottle says. Check out the product's
MSDS to find the real data. Whether the treatment kills fish outright depends on the dose so these products normally say something like "when used as directed".
I've always found it easier to remove living string algae (blanket weed) than dead decomposed string algae.
The green stuff comping off of the dead string algae is mostly settled dead unicell algae. Normally that would settle on the bottom of the pond, but will settle on anything. Think of it as dust. When disturbed it floats in the air or water. Generally it will settle back out of the water in a fairly short time, like maybe 90% in 24 hours.
The more other dead organic matter you remove the faster the remaining will decompose. You can also speed decomposition by lowering dissolved organic matter (DOM, also called dissolved organic compounds or dissolved organic carbon DOC) by employing a "protein skimmer" or "foam fractionator". That allows more O2 into the water which speeds decomposition on remaining matter and also reduces the organic load.
The bottom line is the micro life in a pond can consume a limited amount of organic matter. When overloaded you get stuff like the green dust. Basically you have to keep a pond just about spotless in order for the micro life to consume what remains.