I guess you are asking what's the difference when they both mean "according to".
根據 is like "based on sth., we can get a conclusion or we should do sth."
按照（按、照） is like "following sth."
Most of the time they are just the same, but there might be a nuance.
根據法律，飛機上禁止吸煙 (According to law, it is forbidden to smoke on an airplane)
It sounds more formal. For example, when you are quoting someone academically or giving a judgement based on law, etc.
(按)照他所說的去做 (Do as he says!)
It sounds more conversational. Just like English, you wouldn't say 'Do according to what he says', which sounds quite weird even though the meaning is almost the same. 按照 can also be used as 按 or 照 in casual conversation.
btw, 「他们两个都表示什么不同的意思？」is a grammatically incorrect sentence. It is better to say 「他們兩個有什麼不同嗎？」
and i can't type simplified characters, so please use google translate if you can't read any traditional character