From Spain's perspective that's a distinction without a difference.
If sometime in the past 300 years the British government had formally incorporated Gibraltar into the UK the way Hawaii is a part of the US or French Guiana is part of France, would Spain's complaints about British sovereignty over Gibraltar, and periodic attempts to regain the territory, be any less frequent? I think not.
If sometime in the past 300 years the British government had formally incorporated Gibraltar into the UK the way Hawaii is a part of the US or French Guiana is part of France, would Spain's complaints about British sovereignty over Gibraltar, and periodic attempts to regain the territory, be any less frequent? I think not.