Hmmm. Maybe I should have Googled baby eggplants before making last night's dinner. According to Food Reference :
"Deep purple, round or oval eggplants are often nicknamed Italian or baby eggplants. "
Instead, I used the elongated eggplant, which is, apparently, referred to as the Japanese or Oriental eggplant. I had no idea. More info (that I didn't know) about eggplants here.