One of the many differences (and perhaps most practical to address) is on what Splunk instance each configuration belongs. A practical guide on where Splunk settings should be configured is located on the Splunk Wiki. An overview of the pipelines mentioned in your question can be found in Splunk's online distributed deployment manual.
From a best practice standpoint, we generally keep search time knowledge pieces grouped with parsing configurations and send them to both searchers and parsers in a distributed environment. The parsers are happy to ignore search time pieces and the searchers are happy to ignore parsing configurations. Note: Parsing is usually done on the indexers but if a heavy forwarder is in the data acquisition path, it will do the parsing and send Splunk parsed data.
