“Fancy font” is a useful search phrase, but most copy-and-paste font generators produce Unicode characters rather than font files. Understanding the distinction helps explain why the output can be pasted and why it does not look identical everywhere.
A character is an abstract unit
Unicode assigns a code point to a character. Ordinary capital A is U+0041. Mathematical bold capital A is U+1D400. They may communicate a similar visible letter in casual use, but software sees two different characters.
A glyph is the visible drawing
A glyph is the shape used to display a character. The same character can have different glyphs in different fonts. Serif, proportions and stroke details belong to the font’s design, not to Unicode itself.
A font is a collection of glyphs and rules
A font file provides glyphs, spacing and layout information. When you choose bold in a document editor, the application usually keeps ordinary characters and applies a bold font face or styling instruction.
A Unicode converter instead changes the character. The destination then chooses whatever installed font can display it. You cannot rely on the exact typography shown on the generator page.
When native formatting is better
Use real headings, emphasis and bold controls on websites and in documents. They keep text searchable and usually work better with screen readers, translation and copy editing.
Unicode alternatives are useful when a plain-text field has no formatting controls and the text is short and decorative. They should not replace the semantic structure of a page.
Why the terminology persists
People often call the results “fonts” because they look like type styles. The interface can acknowledge that familiar phrase while clearly explaining that the copied output consists of Unicode characters.