Do Discord’s 256 and 4096 character limits apply to link previews?

Discord does not say so. Those limits are documented for rich embeds sent through its API, and nothing is published for link previews.

Why does my Discord preview look different from this one?

Discord does not document how it builds a preview from meta tags, so there is no specification to match. This preview is an approximation.

Paste a URL to preview an approximation of the Discord card.

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Discord

API embeds

Discord documents limits only for rich embeds sent through its API: 256 characters for a title and 4096 characters for a description.
Link previews

Discord documents nothing about link previews built from a page’s meta tags: no image rules, no tag list and no truncation.
This preview

Because there is nothing to check against, the Discord preview here is only an approximation of the layout and applies no limits.