With a space "breaks" the search; what you are actually asking for is a list of sites that contain the term "www.domain.com" AND "link". Only a query of the form link:
www.domain.com triggers the special syntax
>> Also what the difference if we do this without the www and just have link:domain.com?
Historically, the www. subdomain was used to identify the WWW portion of a domain. The query you reference would generally show up any links you may have to domain.com (NOT the same as
www.domain.com), but that may depend on how your DNS / redirections are being handled