休憩 and 休息: a break and restorative rest
Compare a pause during an activity with rest for recovery.
Pausing an activity
休憩 is read きゅうけい and means taking a break from work, study, travel, or another activity. 「10分休憩しましょう」 proposes a ten-minute break.
「休憩のあとで作業を再開します」 says that work will resume after the break. 休憩 fits a pause within an ongoing schedule.
Resting body and mind
休息 is read きゅうそく and focuses on resting the body or mind. 「十分な休息を取りました」 means that the speaker got sufficient rest.
In that sentence, 十分な is read じゅうぶんな and means 'sufficient,' while 10分 in 「10分休憩する」 means 'ten minutes.' The spelling 十分 can have different readings and meanings depending on context, so check the following form and the situation.
Choosing by focus rather than duration
「休憩時間は十五分です」 announces a scheduled fifteen-minute break. 「静かな場所で休息を取りました」 describes resting in a quiet place.
There is no strict time threshold making 休息 always long and 休憩 always short. Choose according to whether you emphasize a pause in an activity or the act of resting and recovering.
Does a notice saying 「休憩中です」 mean that the work is completely finished?
Show the answer and why
No. It means that a break is currently in progress, usually within an activity. The end of work must be stated separately.

