What is the difference between a sign and a miracle?
They are almost the same. All signs are miracles, but not all miracles are signs.
In the New Testament four Greek words are used for' miracles':
(1.) Semeion, a "sign"; an evidence of a divine commission or message ; a token of the presence and working of God; the seal of a higher power.
( See Mat_12:38-42; Mat_16:1-4 ; Luk_23:8; Joh_2:11, etc.)
(2.) Terata, "wonders;" wonder-causing events; producing astonishment in the beholder (Act_2:19).
(3.) Dunameis, "might[y] works;" works of superhuman power (Act_2:22; Rom_15:19; 2Th_2:9); of a new and higher power.
(4.) Erga, "works;" the works of Him who is "wonderful in working" (Joh_5:20, Joh_5:36).
A 'miracle' is not repeatable in Nature. It is defined in one dictionary as:
" An event that is contrary to the established laws of nature and attributed to a supernatural cause" and in another as "something requiring the suspension or violation of the laws of nature."
A 'sign' is a miracle: it can strengthen a person's faith, be prophetic, and be something to point you to God; however, a sign can be deliberately ignored.
It may help to think of a 'sign' as a 'signpost' : you can look at a signpost and either ignore it or disbelieve it - that is what the Pharisees did. They saw the same miracles as everybody else, but the Pharisees did not want to believe these proofs that Jesus was God in the flesh.
If you don't believe in miracles, then you've missed the signpost.