Despite superficial similarities, non-restrictive relatives and As-parentheticals show contrasting behavior in a range of apparently disparate domains, including (i) equative constructions (Section 4); (ii) Selective Island contexts (Section 5); and (iii) clause-internal "niching" (Section 7). Additionally, As-parentheticals allow a wider range of interpretations relative to their antecedents than do appositive relatives (Section 6). This paper offers a unified account of these differences and others based largely on the respective semantic types of the gaps these clauses define: As-clause traces are propositional, non-restrictive relative traces individual-denoting (nominalized propositions). The type distinction follows from the lexical denotations of these morphemes (Section 2), and combines with independently motivated principles to predict the clauses' divergent behavior. The analysis also unifies the various kinds of appositive-relatives, and similarly informs our understanding of predicate-type As-clauses (Sue hates parties, as does Ali); see Section 8.