How does an imperial crown differ from a regular crown?

Glad you asked!

An imperial crown is closed, comme ca:

The loops of metal over the top, the globe on top, all of these things signify an imperial crown. The symbolic meaning is that the wearer recognized no authority beyond them (save God) – more on this in a second. 

By contrast, a merely royal crown is an open circlet or diadem, comme ca: 

Not to say that royal crowns – like this one, the famed Iron Crown of Lombardy used by Charlesmagne and Napoleon – couldn’t be fancy or important, but they didn’t have the symbolism of imperial rule. 

Why is this symbolism relevant? Well, when England split from the Catholic Church under Henry VIII, part of the legal justification that Thomas Cromwell put together for the Act in Restraint of Appeals was that:

“Where by divers sundry old authentic histories and chronicles it is manifestly declared and expressed that this realm of England is an empire, and so hath been accepted in the world, governed by one supreme head and king, having the dignity and royal estate of the imperial crown of the same.”

Now, keep in mind that some of these “divers sundry old authentic histories” counted Brutus of Troy and King Arthur as examples of British imperial dignity, but Cromwell could point to Henry IV and Henry V, who both were crowned with an imperial crown (probably as an attempt to shore up their authority given the whole business with Richard II), as proof that England had previously claimed independence from the Pope in Rome.