usualy ないしょ　＆　ひみつ　means the same, the sence or feeling or atmosphire is not the same. ないしょ　is usually used more casually, and it sound casually to the person's ear, the main user is children and mother and girls.　秘密　can be used in official document but ないしょ is not.

ないしょ 内所【ないしょ】 (n) kitchen; state of finances. 内緒【ないしょ】 (n,adj-no) secrecy; privacy; secret; internal evidence; one's circumstances; (P). 内証【ないしょ】 (n,adj-no) secrecy; privacy; secret; internal evidence; one's circumstances. ひみつ 秘密【ひみつ】 (adj-na,n) secret; secrecy; (P). 内証【ないしょ】which is limited to internal, 秘密【ひみつ】simply means secret.

I'm pretty sure ひみつ is a secret and　ないしょう is like privacy or doing something in private.