Green Computing is a concept of building computing centres and data centres that have an environmentally sustainable and environmentally friendly role, lowered power consumption which in term reduces CO2 emissions etc.
So the main role is being efficient as much as possible with great concern for the environment. Sometimes, this limits the possibility of handling any workload size due to limited resources.
Grid Computing is a concept of building a number of computing centres and data centres that do not have the aim of being environmentally friendly and efficient, but instead to be modular and to have a large number of independent units which can be turned on and off to handle large and smaller workloads efficiently.
So the main role is being able to scale up and down in order to be able to handle any possible workload equally efficiently, regardless of resources and the environment.
Cloud Computing is similar to Grid computing, but while the whole Grid acts like a "Virtual Super Computer" in Clout computing this virtual entity (the cloud) which is built upon not one, but many grids on different locations (physically), resources are shared between smaller "virtual instances". This way, each instance can be executed on different locations (closest to the client) and can share benefits of large grids (efficient with scalable and flexible workloads).
So the main role is being flexible in terms of scalability so that instances use only those resources they really need and not more, with maintaining the possibility of assigning more resources instantly if workloads begin to fluctuate in order to maintain the same level of efficiency. Just like Grid computing, Clouds seldom care for environmental friendly ideologies. Their main imperative is to be dependant, efficient, flexible, scalable and "always on".
I hope these explanations will suffice to start up your discussion and research study.
Green Computing is referring to ENERGY EFFICIENT COMPUTING. In this type of computing, the end goal is to perform the computations with as few JOULES as possible, by either re-routing the computations to a more efficient destination etc ...
Cloud Computing is referring to "renting computation time" or "renting storage time" from a big cloud operator such as Amazon Web Services (AWS), Microsoft Azure, or Google. Here, you PAY for the services, and you use their infrastructure as long as you are paying. You also use the tools and software they provide you.
Grid Computing is referring to a joint group of computers connected through the internet, dedicated to a purpose. You do not pay for grid computing, and you use their software. Examples are 1) the SETI program by NASA: In this case, any volunteer can contribute his/her computer time to the grid. I think it is called SETI@Home or something. You download the software from NASA, and run it on your computer, and dedicate your down time to their SETI research.
Another example is the TERA GRID, an alliance of a bunch of universities. The purpose is academic, sponsored by one of the government research programs. Again, anybody that wants to use it has to sign up for an academic account, and they are not charged ...
Green Computing is energry saving type of computing, while grid computing aims at developing a complex work handling capable network of computers - much like servers, while Cloud Computing is a virtual storage space. A question therefore is - Is it possible to combine these three aspects of computing and come up with a one system comprising of all 3?
Grid computing system is a widely distributed resource for a common goal. It is Brother of Cloud Computing and Sister of Supercomputer. We can think the grid is a distributed system connected to a single network. This types of computing work with the large volume of files. Basically, it is a cluster types system. So people call it cluster computing.
Grid computer tends to be more geographically disperse and heterogeneous by nature. Grid network also has various types. A single grid is like dedicated connection but a common grid perform multiple tasks.
The size of the grid is large. So grid computing is like supercomputing. It consists of many network, computer, and middleware. Grid computer is dedicated to some specific function of the large volume of data. In the grid process, each task divided into a various process. All the process starts execution simultaneously on a different computer. As a result, very few seconds needs to execute and enjoy the flavor of supercomputing.