You've asked the difference between manager and management. Then you've also asked the difference between management and administration. To understand the difference between both first of all I think it is appropriate to know the meaning of these words. So let me tell you the meanings. When you'll know their meanings. You can differentiate between them easily.
The meaning of management is to progress or to perform adequately especially in some difficult situations. For example, you don't administrate the time. But you manage time and your time table. Now the person who makes management he is called manager. I hope it is clear now.
Second thing you've asked about. It is the meaning of administration. You need to know its meaning to understand it as well. So the meaning of administration is to control, to direct, or to govern. When a person administrate he can be called with both name. I.e. manager or administrator. But there is a very slight difference which I've mentioned. And I hope you'd understand it. And now you can differentiate between them easily. Moreover, I think you can also teach it to other now. I hope I'm right in saying that.
The meaning of management is to progress or to perform adequately especially in some difficult situations. For example, you don't administrate the time. But you manage time and your time table. Now the person who makes management he is called manager. I hope it is clear now.
Second thing you've asked about. It is the meaning of administration. You need to know its meaning to understand it as well. So the meaning of administration is to control, to direct, or to govern. When a person administrate he can be called with both name. I.e. manager or administrator. But there is a very slight difference which I've mentioned. And I hope you'd understand it. And now you can differentiate between them easily. Moreover, I think you can also teach it to other now. I hope I'm right in saying that.