basically although these terminologies are a bit arbitary and context depending, naively speaking: generally, consider that gene set enrichment analysis, which is basically functional/enrichment analysis, includes various gene set testing analysis methodologies, like overepresentation analysis, GSEA, etc. There are some very useful papers or tutorials which you can check:
(* also to mention, in some general descriptions, they have been used described the same thing and have the same interpretation)
Hope this helps,
I am not sure it is the official definition, but in general I use:
- gene set analysis: you have a list of genes (e.g. genes differentially expressed in case vs controls), and you want to know the terms enriched
- gene set enrichment analysis (GSEA): instead of using only the genes that are differentially expressed, you use all the genes analysed, ranked by their expression ratio or by any ranking score, and you get a list of terms enriched in all genes weighting their ranks.