[over.ics.rank] p3.2.1 "Proper subsequence" vs. "subsequence"

[over.ics.rank] p3.2.1

S1 is a proper subsequence of S2 (comparing the conversion sequences in the canonical form defined by [over.ics.scs], excluding any Lvalue Transformation; the identity conversion sequence is considered to be a subsequence of any non-identity conversion sequence) or, if not that,

It seems "proper subsequence" has a stricter meaning than "subsequence". The intent of this provision is to say that [over.ics.rank] p3.2.1 will be applied to if S1 is an identity conversion sequence while S2 is a non-identity conversion sequence. However, according to the sentence in the parenthesis: the identity conversion sequence is considered to be a subsequence of any non-identity conversion sequence. It did not say it's a "proper subsequence".

Should we change the definition to that

S1 is a proper subsequence of S2 (comparing the conversion sequences in the canonical form defined by [over.ics.scs], excluding any Lvalue Transformation; the identity conversion sequence is considered to be a proper subsequence of any non-identity conversion sequence) or, if not that,

Start at [over.ics.rank] p3.2.1 and compare its use of “proper subsequence” with the parenthetical reference to [over.ics.scs]. Determine whether the identity/non-identity case is intended to require a proper subsequence, then update the standard wording if appropriate. Done means the terminology clearly expresses the intended conversion-sequence relationship.