Call them "Unicode fonts" and typographers will wince — because no fonts are involved. A font is a file of glyph drawings that an app chooses; you cannot copy a font into an Instagram bio. What you can copy are characters, and that's the trick every text style generator uses.
Character substitution, not styling
When this site converts "cat" to "𝓬𝓪𝓽", it replaces each letter with a different Unicode character that happens to look like a styled version of it. The letter c (U+0063) becomes the mathematical bold script c (U+1D4EC). Your clipboard carries those code points, and every app that receives them renders the script look.
Three families of tricks
Parallel alphabets. Bold, italic, script, fraktur, monospace, double-struck and sans-serif alphabets exist as complete A–Z sets in the Mathematical Alphanumeric Symbols block. Conversion is a simple one-to-one mapping.
Combining marks. Underline, strikethrough and glitchy zalgo text attach combining characters — marks that render on top of the previous letter. An underlined a is really two characters: a + U+0332.
Lookalikes. Upside-down and mirror text have no dedicated Unicode block. Generators improvise with visually similar characters from other alphabets: the upside-down e is actually ǝ, a letter used in Azerbaijani.
The limits
Only characters Unicode actually encodes can be produced. There is no bold comma, no script digit set for every style, and no subscript b. Good generators pass unmapped characters through unchanged rather than faking them. Rendering also depends on the destination: a rare glyph missing from a device's fonts shows as a box (□), and heavy combining-mark stacks may be trimmed by some platforms.