How to make more than one part with same design which only differs in dimensions???

If I understood your question. You can open folder which contains part you want to change. Copy that part multiple times and go to new copied parts and change dimensions as you wish.
Other way is to open that part you want to change. Change dimensions and then go "Save as" and choose folder and name of part, you may do it multiple times in one session. Important is not to save file as standard "Save" when you are finished with changing dimensions because that will change original file.
There is a way to change dimensions with equations, but you still have to use option "Save as", as far as I know.
Hope this helps.

If you are looking to do this with one part file, it can be done with a design table or multiple configurations. There are tutorials within Solidworks that can help you learn how to use these features.

Mark Burke is correct. configurations is the best way. link each dimension to a name.
Add your configurations for all different parts. Right click on the variable dimension and select configure dimension. In the table edit the dimension for each configuration.