Full Idea
The difference between the principle of consistency and the principle of non-contradiction is that the former must be stated in a semantic metalanguage, whereas the latter is a thesis of logical systems.
Gist of Idea
Consistency is semantic, but non-contradiction is syntactic
Source
Edwin D. Mares (Negation [2014], 2.2)
Book Reference
'Bloomsbury Companion to Philosophical Logic', ed/tr. Horsten,L/Pettigrew,R [Bloomsbury 2014], p.184