Without

ないで

Means “without doing”. Formed with a verb in the negative tense (ない). It is a bit more casual than ずに.

Example

勉強べんきょうしないで卒業そつぎょうした。 I graduated without studying.

ずに

Means “without doing”. Formed with a verb in the negative tense (ない) by removing the -ない stem and adding ずに. する transforms to せずに. It is a bit more formal than ないで.

Example

毎日食べずに出かける。 Everyday, I go out without eating.