Hi. I don't think there is any categoric answer to your question. Different people might well have different opinions, and there is no single absolute authority on paperweight terms - just 'common usage', which can vary from country to country!
For me, the key points of a crown are that there is a broadly spherical structure made of parallel staves (which may remain straight or be made with some twist). The millefiori cane on top is just a practical means of hiding the join - but can add to the overall attractiveness if chosen carefully. The Murano paperweights that are ovoid, with a loose latticino spiral, would not count as crowns for me, for example.
I have attached images of two paperweights from my 'Murano project' pages, which - to me - are a crown, with a millefiori centre, and a spiral. Others may not agree!