What makes fleur de sel different from regular salt?

I'm not 100% sure but I found this site that explains what fleur de sel is. It says that

Like other sea salts, fleur de sel is harvested by evaporating sea water. However, to harvest fleur de sel, workers gently skim the top layer of the sea salt from partially evaporated pools, before it sinks to the bottom again. These salt crystals are very fine, light, and delicate, and must be handled with care and exposed to minimal moisture, or they will clump again.

It looks like you are reproducing how fleur de sel is made, through boiling the water which is the equivalent to "evaporating sea water".

1. It is harvested manually
2. It is a small portion of the evaporated sea-salt produced.
3. It is a lot more expensive
4. It has finer salt-flakes as normal evaporated sea salt.

Unless you can distinguish it from other salts in a double blind randomized controlled trial I do not think that it is worth the trouble. Setting a trail up with a few friends is a lot of fun :)

AFAIK, the mineral content of the salt is the major difference. Also, the smaller crystals of Fleur de sel dissolve very quickly.

There is an incorrect assumption in your question. Fleur de sel (flower of salt) is not salt collected from the top of a boiling pot of salted water. It's salt collected from evaporated ocean water. This is important and contributes to the following differences:

1. The mineral content of the ocean is different than the contents of a pot with water and table salt. So the final salt is composed of more than just sodium chloride. Fleur de sel also includes calcium, magnesium, potassium, and iron.
2. By virtue of the collection method and the fact that it is not agitated by boiling but evaporated by the sun, the structure of the flake is very specific. Delicate "flowers" of salt that are texturally distinct from grains of table salt or flakes of flaked salt.
3. Fleur de sel is formed in open air ponds. The resulting salt contains biological material as a natural side effect of it being made outside.

It's a specialty product. It's harvested by hand on nature's schedule. The sun is the heat source. Winds can disrupt the formation of the flowers. It's expensive.

Most importantly, I just tasted Maldon flaked salt, kosher salt, and fleur de sel back-to-back while writing this answer. They taste different. That's probably the most important thing to note.

Since the salt crystallizes in a manner that produces large flat flakes it makes it ideal for finishing a dish since it offers a small textural contrast while providing good salt coverage. Compared to coarse kosher salt it provides a small crunch and adds texture to the dish without being overwhelming it. It's also visible versus something like a fine grained table salt. It's a finishing salt though, so get some nice cheap fine grain salt for your regular day-to-day needs, and keep your fleur-de-sel in a small pinch pot to throw on finished dishes immediately before serving.