It seems they both mean busy. Can someone tell me what the difference is between them?
They are slightly similar but Nigiyaka also has the meaning of lively or "genki". Isogashii feels a little more like a negative way to say busy, while nigiyaka might seem more positive.
For exemple, isogashii would be used for work(negative) while nigiyaka could be used for a party or a parade as meaning crowded/busy(positive)
Another more practical difference would be that isogashii can be used for people, and nigiyaka for events/places. I'm busy(isogashi) / the office is busy(nigiyaka)
忙しい is busy.
賑やか ejje.weblio.jp › 英和辞典・和英辞典 › 賑やかの意味・
そこはとても賑やかです。 It was very lively there. - Weblio Email例文集.
( 実に賑やかな男だ He is a lively fellow―a merry fellow. - 斎藤和英大辞典. )
( 人の様子が賑やか of a person being cheerful ) - ...
We usually don't think of 賑やか as busy.
----- 賑やか is busy in the sense of (a parade, shopping center, ... (rather than a person) ... being) lively, bustling, full of life and colors, cheers, activity, mirth, ... .
A busy street (or a busy office) is not 賑やか if it's grey and depressing.
When a person is described as 賑やか -- it's a description of his/her personality.
When a person is described as 忙しい -- it's a description of how he/she is at the moment.
A person who seems / appears busy all the time (like personality) "a restless / fidgety person" is せわしない人 ( 忙しない人 ) or せわしい人【忙しい人】 -- (the former is perh. Kansaiben).