Isogu is definitely "hurry", yes, but "hayai" doesn't only mean "fast". It can be used meaning "early", like "Hayaku okiru" (wake up early) "Hayaku dekakeru"(go out early)... we have two Kanji to explain "hayaku""hayai". The one is ”早い”, related to time(early or late). The another is ”速い", explains speed(fast and slow).

"hayaku(hayai)" is like "fast". "isogu" is like "hurry", and contains "an intention; a wish; a purpose" "isogu" means "to do something fast". The car runs fast => hayai You shuould go hurry => isogu I hope this will be your help.