correction in verbiage:
Non church accounts do not have your lds membership number attached
as such - the system assumes that account is NOT for an LDS member - and does not display any related info that would be for members (such as LDS ordinance info)
Short Answer: We ALL (Users/Patrons) have a FREE 'Account' in 'FamilySearch'.
The 'Accounts', of Members of the Church, who are Users/Patrons, just have some EXTRA features/functions/facilities, that are to do with our Church beliefs.
Those EXTRA features/functions/facilities, that are to do with our Church beliefs, are just not, accessible; or, seen, by Users/Patrons who are NOT members of the Church - as, there is NO need for such - it is nothing, secret or untoward.
Is that what you are referring to?
Or, are you referring to Partner websites?
The only difference between a member and non-member *Family Search *account is no LDS information displays on non-member account. Sign in is the same, sources are the same, memories are the same.
Surprisingly, a non-member can sign-in by clicking on "Sign In with Church Account". I tried this just now, to confirm I had done so in the past. However, everything looks just the same as if I had signed in my usual way - using my "public account". My memory might not be correct, but I thought (when I signed in via "Church Account" previously) I received more LDS orientated messages, but certainly I had / have no view of any ordinance detail that might relate to some of my relatives. Oh, and there are no "extra privileges", like being able to view restricted images available only to LDS Church members!
In short, for non-members it seems to make little or no difference which account you use to sign in to FamilySearch.
In indexing it does make a difference if you sign in with your LDS account number. You may have access to more projects to work on than those of us with non-member accounts. For instance, as a non-member I cannot index the Wisconsin state records.
in my response when I said LDS account - I was simply referring to an account that has a membership number attached to it
I was not focusing in how they logged on - but if they had a membership number
as you point out - they can still log even with the method that says LDS account - but when they do the system still recognizes the account is not linked to a member and treats them as such,
All accounts with access to FamilySearch.org are free "Church Accounts" and are managed within the same account system regardless of Church membership.
If the account has a Church Record Number (Membership Number) associated with it (a Member Account), that account has access to Church Specific applications and information. If the account doesn't have a Church Record Number in it, then it is designated as a "Public Account" and has access to publicly available information in FamilySearch.
There are different roles even within member accounts depending on what the member is authorized to do in service of the Church and the account security system either grants or restricts access to information and applications based on the user's role.
Help Center Article for creating a free account as either a public account or a member account:
Public account holders who are members can add their membership number to their existing public account. However, if they already have an account with their membership number in it, they cannot add it to another account until they delete the existing member account--which is not encouraged due to the information lost when an account is deleted.