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.