Are these fonts or characters?

Characters. Each styled letter is its own Unicode character with its own code point and name.

Why are some letters missing in a style?

Unicode added these alphabets for specific uses and didn't always include every letter or digit. The cards say what's borrowed or missing.

How Fancy Text Works — Unicode, Not Fonts

𝕱U+1D571Mathematical Bold Fraktur Capital F

𝖆U+1D586Mathematical Bold Fraktur Small A

𝖓U+1D593Mathematical Bold Fraktur Small N

𝖈U+1D588Mathematical Bold Fraktur Small C

𝖞U+1D59EMathematical Bold Fraktur Small Y

No font is involved. Each letter is a separate character that Unicode added for mathematicians, with its own number and its own name. That is why it survives copy and paste into apps that do not let you choose a font.

Where each style comes from

Style	Unicode block	Why it exists	Gaps
𝐁𝐨𝐥𝐝 𝐼𝑡𝑎𝑙𝑖𝑐 𝓢𝓬𝓻𝓲𝓹𝓽 𝔉𝔯𝔞𝔨 𝔻𝕠𝕦𝕓𝕝𝕖 𝚖𝚘𝚗𝚘	Mathematical Alphanumeric Symbols (U+1D400–1D7FF)	Math notation, where bold v and script v mean different things	24 letters were already in Letterlike Symbols and are borrowed from there; no italic or script digits
Ⓑⓤⓑⓑⓛⓔ	Enclosed Alphanumerics	Older East Asian character sets	None for letters
🅑🅛🅐🅒🅚 🅂🅀	Enclosed Alphanumeric Supplement	Japanese TV and phone symbol sets	Capitals only
Ｗｉｄｅ	Halfwidth and Fullwidth Forms	Latin letters in the square grid of CJK text	None
ꜱᴍᴀʟʟ ᵗⁱⁿʸ ₛᵤb	Phonetic Extensions, Spacing Modifier Letters, others	The International Phonetic Alphabet and dictionaries	Patchy: no superscript q, subscript for 17 letters
S̶t̶r̶i̶k̶e̶ U̲n̲d̲e̲r̲	Combining Diacritical Marks	Accents that attach to the previous letter	None, but joins depend on the font
ɐɟ ʇ	IPA Extensions + assorted look-alikes	Phonetics; the flip is a visual trick	Several letters borrowed from unrelated scripts

Why some people see boxes

A character only shows if a font on the reader's device contains it. Phones and computers made in the last several years cover all of these blocks; older Android versions, some smart TVs and some car screens don't, and draw an empty box (“tofu”) instead. You can't fix that from your side, which is one more reason to keep the important words plain.

Nothing leaves your device

The tables load once with the page (about 15 KB). Converting, copying, pinned styles and your last text all live in your browser. “Copy a link to this text” puts the text after a # in the link, a part of the address browsers never send to the server.

Sources: Per Axbom, “Don’t fake bold and italic text with Unicode”; Unicode Standard, Mathematical Alphanumeric Symbols chart.

Questions

Are these fonts or characters?: Characters. Each styled letter is its own Unicode character with its own code point and name.
Why are some letters missing in a style?: Unicode added these alphabets for specific uses and didn't always include every letter or digit. The cards say what's borrowed or missing.