U+1D400 The Unicode codepoint the style's characters come from. Two styles can look almost identical and still be different characters with different device support. The codepoint is the only reliable way to tell which one you copied.
IGTTRB Platform support. Green renders reliably. Amber works, but breaks on some devices or in some fields. Struck through is filtered out or rejected by that platform.
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The same style inside each frame. Type above and these update with it, then tap to copy the whole thing. The number is the character count, which matters if you are pasting into a field with a limit.
Script is the style most people mean when they say cursive, and it is the one where Unicode's history is most visible in the result. It begins at U+1D49C, but eleven of its positions were already occupied when the mathematical block was defined in 2001. Those characters had been allocated years earlier in Letterlike Symbols, so the standard left the maths positions reserved and the letters have to be borrowed back from that older block.
The borrowed characters are B, E, F, H, I, L, M and R in uppercase, and e, g and o in lowercase. They were drawn at a different time by different hands for a different purpose, so at larger sizes they sit slightly differently in weight and slope from the rest of the alphabet. This is not your device rendering something wrong; it is a seam in the standard itself, and every tool that offers this style has it.
Support is good but not universal. Script is one of the styles most likely to fall back to a substitute font on older Android builds, and when it does the result looks uneven rather than simply missing. You get letters, but from two different sources. Digits are not covered at all, so numbers in your text stay plain.
If you want cursive without the seams, bold script starting at U+1D4D0 is fully contiguous with no borrowed characters, which is a large part of why it became the more popular of the two.
Eight uppercase and three lowercase letters are borrowed from the Letterlike Symbols block, because their positions in the mathematical block were already taken by characters added to Unicode earlier. Different origin, different drawing. It shows most at larger sizes and it affects every tool offering this style.
Script has no digit forms in Unicode, so numbers pass through as plain text. If your text contains numbers and you want them styled too, bold, monospace, double-struck or fullwidth all include digits.
Bold script is contiguous with no borrowed characters, so it renders more evenly, and it is the more widely used of the two. Plain script is lighter and less assertive, which suits some contexts better, but expect the seams.