Tilde immediately followed by a newline ignores the newline and any following non-newline whitespace_1 characters. With a :, the newline is ignored, but any following whitespace_1 is left in place. With an @, the newline is left in place, but any following whitespace_1 is ignored. For example:
(defun type-clash-error (fn nargs argnum right-type wrong-type) (format *error-output* "~&~S requires its ~:[~:R~;~*~]~ argument to be of type ~S,~ with an argument of type ~S.~ fn (eql nargs 1) argnum right-type wrong-type)) (type-clash-error 'aref nil 2 'integer 'vector) prints: AREF requires its second argument to be of type INTEGER, but it was called with an argument of type VECTOR. NIL (type-clash-error 'car 1 1 'list 'short-float) prints: CAR requires its argument to be of type LIST, but it was called with an argument of type SHORT-FLOAT. NIL
Note that in this example newlines appear in the output only as specified by the ~& and ~% directives; the actual newline characters in the control string are suppressed because each is preceded by a tilde.