An American with a British parent may already have been a British citizen from birth. Another person with an apparently similar family history may need to register. A third may have a UK-born grandparent but no present citizenship route. The outcome turns on the legal chain, not the strength of the family's cultural connection to Britain.
The distinction matters because a passport application proves an existing status, while registration creates citizenship from the statutory event or ceremony. An application under the wrong category can obscure a valid claim, invite irrelevant evidence or fail to address the historic rule which prevented citizenship passing through the family.
For US-based families, the analysis should also be completed across generations. Establishing that the parent is British by descent may resolve the parent's position but leave a child born in the United States without automatic citizenship. That child may instead have a time-sensitive registration entitlement based on the British parent's residence or the family's later residence in the UK.