with-in group, between group

within subject design = participants are involved in all conditions in a study, e.g. when a study is about how noise affects memory, and there are two conditions (no noise and noise), each participant will be asked to do both conditions one after the other

between subject design = participants only involve in one of the many conditions, e.g. either the no noise or noise condition. One advantage is, there's no practice effect, where within subject design participants will know what is expected after one trial, but this can also be eliminated by counterbalancing. One disadvantage of between is, you can't tell how one might improve in two conditions, because different people were involved in the two conditions.

with in group means you are in the group of a project while between group means you are between group of strangers