A Dyson swarm is a subcategory of Dyson sphere. The swarm is oriented around the Sun (or star) in a spherical shape.

The idea of a solid spherical object or single 'Ringworld' like habitat is not what Dyson originally had in mind when he proposed looking for these throughout the cosmos. In fact, he was thinking that the civilization would gradually create more and more orbital habitats, each with its own set of solar collectors. He estimated that disassembling all of the planets in the solar system would yield enough for around three meters of average thickness. That is, you could have thin solar mirrors covering most of the area, with thick, well shielded habitat areas and buildings on the inside in smaller regions.

A more modern concept of Dyson sphere called a Dyson 'bubble' is much more easy to make because it sticks to a closer distance from the Sun than Dyson's 1.0 AU estimate, and it uses a much thinner type of solar panel that uses much less materials, being just a few microns thick. Today we know there is a special substance called graphene that can support a 4 kilogram object in a 1 square meter sheet, despite being a nanometer thick, weighing 0.77 milligrams. The sun puts out a constant amount of light, which repels objects at an acceleration rate equivalent to the gravity times about 0.78 grams per square meter, so the optimal average weight of a stationary (nonorbiting) power collection station would be about 1000 times that of a sheet of graphene. That extra mass could be something like a thousand layers of graphene, or (to save carbon) could just be metal or glass of a type that is abundant throughout the asteroid belt.

The amount needed to build a structure of this scale, with a distance of 0.3 AU from the Sun, is around a tenth that of the second largest asteroid. That's big, but not nearly as big as people often claim. The video claims that it would be 'all the terrestrial mass in the solar system', but this is simply not supportable -- we are talking about a fraction of 1% of a terrestrial planet. On the other hand, it does give us enough energy to disassemble entire planets in a short time frame -- if we feel the need to do so.