Later in the sleep-deprived fetish episode (in S02E05) Kaguya calls 'true love' as 本物の愛 (I think honmono no ai and ほんもののあい). The narrator also calls this 'true love' (in katakana トウルーラブ) and 'eternal love'.
(Also, for some reason, the narrator seems to introduce 2 other terms 真実の愛 - しんじつのあい shinjitsu no ai translated as 'real love' and 永遠の愛 - えいえんのあい eien no ai translated as 'eternal love'. Note the shinjitsu no ai vs shinjitsu no koi.)
What's the difference between S01E01 真実の恋 and S02E05 本物の愛 ?
In particular, what makes the latter 本物の愛 so 'cringe' or something? Is the former just as cringe? Or what? See what 2 of the other characters Nagisa (Kashiwagi) and Chika (Fujiwara) think about 本物の愛:
Nagisa says 'She actually said "true love"!'
Chika says 'Aren't you a little too old for that?'
What I got so far:
I know the Japanese language brilliantly has specific words for 'like'/'love' like suki, daisuki, aishiteru, koishiteru. In the latter 2 words, we can of course see the respective roots 'ai' and 'koi'.