People get confused about this seemingly simple question. I hear people saying that BLAST performs a local alignment, but FASTA performs a global alignment. Also, historically there seem to be different versions of FASTA with different behaviour. I would like to hear an expert opinion on this.
You don't have to be an expert; it's right there on the web pages and in the documentation.
The FASTA programs find regions of local or global (new) similarity between Protein or DNA sequences
So originally, FASTA did perform local alignment, but more recent versions also perform global. You can also read the changelog to see revisions over time.
The Basic Local Alignment Search Tool (BLAST) finds regions of local similarity between sequences