SAP provides a lot of offerings which are industry specifics and can be altered/ modified within limits to serve the purpose. Offerings include industries ranging from Sales, HR, Plant maintenance and others. One can customize the existing system to serve the needs but the customization is not extensive and basically revolves around a change in settings, altering configuration tables and adding custom things.
You can develop custom things to serve a requirement which is out of the box. SAP provides a complete development environment. The same environment is used to develop the standard offerings so we can create our own custom one (for sure it will not be an easy task in any way) and which can work in sync with other existing standard offerings. Custom programs, routines, modules, reports etc. - most of these can be created.
The other way is not the hectic one of creating a new implementation altogether but to modify the standard implementation. It has to be really careful as we are making the modification to standard implementation; there are chances that it might affect the standard implementation functionality and performance.