business methodology - is a system of broad principles or rules that is PURPOSE BASED which specific methods or procedurces.
Process Improvement is the proactive task of identifying, analyzing and improving upon existing business processes within an organization for optimization and to meet new quotas or standards of quality.
It often involves a systematic approach which follows a specific methodology but there are different approaches to be considered. Some examples are benchmarking or lean manufacturing, each of which each focuses on different areas of improvement and uses different methods to achieve the best results. Processes can either be modified or complemented with sub-processes or even eliminated for the ultimate goal of improvement.