We have a variety of overlapping and confusing concepts. Here I'll briefly attempt an explanation of the current state of things. We can then discuss and iterate
Account
The most commonly-used term. An account always has a key, which is used to derive the account ID (public key).
An account is sometimes a person, company, or device
Site
Generally used to refer to the Account + the documents that the account owns. It is logically equivalent to the "website", which represents the authority as well as the content on a particular domain.
Space
Usually means the same as Site but it is not formally defined.
Profile
The public information about an account that has been published. You can publish a Profile with a name, icon, and other metadata.
Redirect Profile
In the case of a device account, the profile is a redirect to the main account which is used to identify this person/company.
Basically a redirect profile is used to say "this account is really this other account"
Note: a redirect document may also be published, but this is a distinct concept from Redirect Profiles.
Contact
A contact is a relationship between two accounts. It is a publishable resource with an ID. It stores the "edge name" of the person.
So, Alice may publish a Profile with the name "Alice A." and Bob might publish a Contact with the name "Good Alice", to differentiate with other Alices.