Just assume we are installing some libraries from its source distributed by the way GNU promoted. When using "./configure --prefix" to specify where to install.
(1) does Make generate the binaries under the current directory? Does Make install then copies them from the current directory (which is from where Make is run) to $prefix? If the answers are yes, I have two questions, each for different cases.
(2) when the current directory and $prefix are not the same, can I remove all the files generated by Make under current directories to save some space?
(3) when the current directory and $prefix are the same, will make install do nothing or copy the files to themselves? Can I just skip the make install step?
You are absolutely right: make just creates files in current directory and make install copies it to the destination directories, based on $prefix and other variables maintained by configure script.
You can wipe out the whole directory you've ran the build at. It will not be used, because, well, that's what "install" means: you build in one directory and the the files are placed in the proper places of your system.
Usually install destination and the directory you build in differ. The hierarchy of the files being installed usually do not relate to directory hierarchy of the build system. Just install to the other dir: it's cheap to create just yet another directory.