Gene Ontology web specifically states that "a biological process is not equivalent to a pathway". They also state in their mission statement that "The mission of the GO Consortium is to develop an up-to-date, comprehensive, computational model of biological systems, from the molecular level to larger pathways, cellular and organism-level systems." and mention the term pathway in other sections.
I assume that GO Biological Processes are not equivalent to pathways but how are Biological Processes and pathway related? are biological processes part of pathways?
The word pathway used in the sentence you quote from the GO consortium doesn't have the same meaning as the word "pathway" as it refers to the KEGG term you link to.
The term "pathway" is common-usage word that is used in any number of different ways by any number of different groups of people/databases, where as the term "GO Biological Process" has a very defined meaning (defined by the GO Consortium). There are many different databases that claim to provide information about pathways e.g. KEGG, WikiPathways, IPA, Pathway Commons, etc. Each one probably has some subtly different idea about what they mean by the word pathway (I'm pretty sure several havn't ever really considered what makes something a pathway). Its important to realise that "pathway" is a human defined concept, and they probably don't ever correspond to a concrete, biologically isolatable reality.
That said there some things that I think most people would think applied to a "pathway", that other gene sets done. In a gene set defined by a shared GO term, nothing is implied about the relationship between genes within the set, other than the property of sharing some connection to the function implied in the go term. I think its reasonable, on the other hand, that for something to be called a "pathway", there must be some information about the ordering and relationship between the genes in the pathway i.e. A activates B, which represses C etc. These relationships don't have to be linear, but I think the word "pathway" implies that they are directed, and that pathways have inputs and outputs.
There are two different consortiums all together friend. the Gene Ontology identifiers start with GO, while KEGG start with KO. GO terms tend to be more specific most of the times, depending how deep in the hierarchy you go into, while KO terms tend to be more broad. Their organization is different, and there might be overlaps across all three GO parent categories (Biological Process, Molecular Function and Cellular Component) with the KEGG pathways, but the both databases are not related in any way.
