Loli

Loli came from 'Lolicon', which also originated from the 'Lolita Complex'. In terms of Japanese culture, 'Lolita' was taken from Nabokov's novel but instead stems from the positive idealization and romanticization of girls' culture developed during the Meiji period. 'Complex' derives from 'romantic love for something'. So, that's how it came into existence. It was shortened to 'lolicon', as the Japanese refer to having a complex of loving physically young-looking girls. With time, it evolved into the word 'Loli'.

A: "Hana-san is so small, she not able to take document at high place"
B: "I did saw too, that loli also been confuse as high school girl"

Shota

Shota came from 'Shotacon', which also originated from the 'Shōtarō Complex'. 'Shōtarō' means 'masculine young man', and 'complex' derives from 'romantic love for something'. So, that's how it came into existence. It was shortened to 'Shotacon', as the Japanese refer to having a complex of loving physically young-looking boys. With time, it evolved into the word 'Shota'

A: "Did you seen Yamazaki-kun worked in IT department? He looked very young and short"
B: "Yamazaki-kun is Shota