I think there are over 10 varieties of eggplant/aubergine. I've used the one in your photo for making Hyderabadi eggplant "ka salaan", for stuffing with coconut, onion, palm sugar, tamarind and fresh chiles; for making Kashmiri sweet/sour eggplant...He called the small purple things apple eggplant, but I've only been able to Google apple green eggplant.
Not sure what to do with them...
You can use them just as you would a regular eggplant.