EQUALP function compares same things as equal, additionally result is true under some other situations: conses are compared recursively (in both car and cdr part), any sequence is compared recursively (element-wise), strings and characters are compared case insensitively. Result is true if they are same, otherwise false.

(equalp "moo" "moo") => T
(equalp "moo" "MoO") => T
(equalp "moo" "moo ") => NIL
(equalp (vector 2 3 4) (vector 2 3 4)) = T
(equalp (cons 1 2) (cons 1 2)) => T
(let ((x (cons 1 2))) (equalp x x)) => T

(equalp 'moo 'moo) => T
(equalp 'moo 'foo) => NIL
(equalp "a" 'a) => NIL
(equalp 1 1) => T
(equalp 1 2) => NIL
(equalp 1234567890123456789 1234567890123456789) => T

(equalp 1.0 1) => T
(equalp 1.0 1.0) => T