An イヤリング is an ear accessory that does not require a piercing. The word refers only to accessories worn on the ear.

A ピアス is jewelry worn through a piercing, whether on the ear or elsewhere on the body.

Further Reading

Examples

A picked-up earring with イヤリング

Learn the meaning and usage of the vocabulary イヤリング vs ピアス in Japanese, with examples from manga.
俺物語!! » Volume 4 » Page 92

Takeo runs after a mother and her child to give them a shoe they dropped. Due to Takeo’s large size and loud steps, the mother and child get frightened and run from him. After he manages to return the dropped item, Takeo returns to his friends. Rinko remarks that the scene was like “A Bear in the Forest”. Sunakawa recalls the song.

砂川(すなかわ):
「あーイヤリング(ひろ)って()いかけるやつね」
“Ah, the one who picked up an earring and chased after.”
猛男(たけお):
「そうか (くま)だと(おも)われたのか」
“I see. It's that I was thought of as a bear?”

Bead as an earring with ピアス

Learn the meaning and usage of the vocabulary イヤリング vs ピアス in Japanese, with examples from manga.
好きな子がめがねを忘れた » Volume 5 » Page 56

Komura sees Mie pick up an item she dropped and he wonders if it’s an earring. During class later, Mie shows Komura the item held up to her ear calling it a 「ピアス」. She then reveals it’s just a bead.

三重(みえ):
(わたし)ピアス()けてないし」
“Since I don't have my ears pierced.”
小村(こむら):
「あっ… …今朝(けさ)()としてたのもビーズ?」
“Ah, the item you dropped this morning was a bead?”
三重(みえ):
「うん」
“Mmhm.”