Both IHS and JHS signify, in the Latin alphabet, the first three letters of Jesus' name in Greek.
In Christian art, often the letters IHS or JHS are used to represent the name of Jesus.
Is there a difference between IHS and JHS?
Starting in the 3rd century, Christians shortened the name of Jesus by only writing the first three letters of his name in Greek, ΙΗΣ (from his full name ΙΗΣΟΥΣ). The Greek letter Σ (sigma), is written in the Latin alphabet as an “S,” resulting in the monogram being commonly represented as ΙΗS.
One of the main reasons this monogram has the letter “I” in it is because both Greek and Latin did not use the letter “J” for many centuries.
According to Latin scholar John Byron Kuhner, in an article for Inside the Vatican, this issue came-up when St. John Paul II wrote his name in Latin using a “J.” At the time, Fr. Reginald Foster was at the Vatican and pointed out the error.
“In 1978, after John Paul II was elected, he has to sign his first document, and he writes a big long loopy ‘J’ as the first letter. Now we all look at each other, and send the thing back. We say ‘We’re very sorry but there’s no ‘J’ in Latin, your Holiness. Your name is IOANNES, not JOANNES.’ Well, we get a note back from him saying, ‘Quod scripsi scripsi.’ ‘What I have written, I have written.’”
By the 16th century the letter “J” became used in many Latin inscriptions, including the “JHS.”