BLAST and FASTA similarity searching for multiple sequence alignment.
There is whole lot of easily accessible knowledge available on Google if you want to really get answers. No one can actually make you understand the algorithm here.
Both FASTA and BLAST are algorithms for searching local similarities between a query sequence and those within a sequence database. Every query sequence is somehow compared to all sequences in the database but in a one-to-one fashion. On the other hand, multiple sequence alignment is the process for aligning simultaneously a number of assumed homologous sequences. So FASTA and BLAST are not algorithms (programs) for multiple sequence alignment. Typical programs for doing this are ClustalX, Muscle, Mafft, etc.
FASTA algorithm is kind of obsolete these days. The only reminiscense still in use is the format associated to that name. So I recommend you studying BLAST instead. If you want to really understand the logic behind BLAST I recommend you this article:
Pertsemlidis, Alexander, and John W. Fondon. "Having a BLAST with bioinformatics (and avoiding BLASTphemy)." Genome biology 2.10 (2001): reviews2002-1.
Best regards.
Please read the attached article carefully.
Sequence Similarity Searching, https://www.ebi.ac.uk/Tools/sss/
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