There is no such thing as DeleteOnSubmitand in ASP.NET MVC DeleteAllOnSubmit, so I assume that you mean the methods in LINQ to SQL tables. (Correct me if not.)
Basically you use DeleteOnSubmitto delete a single row from a table, specifying a single object that maps to the row you want to delete.
DeleteAllOnSubmit , , , IEnumerable<> , , . (List<T>, Collection<T> .)