As a native mandarin speaker, I can tell you that when you ( say Spa Owner) say 帶走, it's more in a tone of being polite for a kind reminder to guests, while 拿走 is in a tone of thinking you're likely to mis-behave and as if I were saying it to your face. After all, difference is subtle and they can be both used, but a tone of degree of aggressiveness in reminders can vary in this situation. 帶走 is polite 拿走 is less polite and may sound more direct to someone.

It will still be correct to say"拿走". The difference is very subtle in this situation. 拿put more emphasis on the action of taking things away.

It will still be correct in this situation. If u want to say"Take 2 apples away from 5 apples, there're still 3 apples. " You must say "从五个苹果中拿走两个，还剩三个That's beacause when saying you takes away the apple, you dont carry it to another place. But when you bring some apple from your home to school. You could either say 我从家带了一个苹果 or 我从家拿了几个苹果 In this situation, the sign want to tell you not to bring the 桑拿沐浴用品to somewhere else. So both 拿走 and 带走is ok.

Please do not take the sauna, and please do not take the sauna. The two sentences are the same in meaning, but taking away and taking away here mean taking or taking away without the consent of the owner of the goods. The correct meaning of taking away and taking away here is not to be sneaked away , There is the meaning of theft, but in order to be good to read so take away, this should be for Chinese people can understand this Do not take away representative Do not steal, If a separate translation I directly explain the Chinese dictionary it simple Belt is 1. With the skin, cloth or thread made of long strips. Like a long strip of material. 3 car tires. 4. Area. 5. Wear, put on. Hold with you. 7. Take along, attached, by the way to do. 8. Containing, rendering. 9. Lead, guide. Take 1. Take by hand, hold in your hand. Grasp 3. Relying on (xié) system. 4. Erosion, damage. Arrest, catch. Capture, occupy. . Prepositions, leads by virtue of the tools, materials, methods, equivalent to "use." Your belt here is the 6th translator, a single one generally refers to the stripe, and when it is added, it becomes a verb Take the first translation, generally take refers to the verb, I personally do not understand English, so I am typing. I do not know if I'm in English with Google Translate. I hope you will not be more confused

actually, 拿 = take， 带 = belt. such as 腰带。 visually，带走 = you take something and put it in your package whose shape is long strip like a belt around your waist. so it has the subtle meaning of "Incidentally", "by the way", "steal". for examples: 顺带一提，你出去的时候请把门带（close it incidentally）上 拿 = you just take it in your hand. in a word, they are same in daily practice.