As adverbs the difference between hereinto and thereinto
is that hereinto is into this circumstance, matter, place, or situation; into this while thereinto is into that place, state etc.
hereinto
English
Adverb
(-)
Into this circumstance, matter, place, or situation; into this.
thereinto
English
Adverb
(-)
(archaic) Into that place, state etc.