Alignment of sequenced fragments in Next Generation sequencing (sequence assembly)
Assembly and alignment are generally used to refer to two different algorithms that work in two different ways.

Alignment takes your sequence fragments, and compares them to a reference genome, and tells you where that read aligns and how closely it aligns.  For a while, popular aligners used Burrows-Wheeler transform algorithms to make special indexed versions of the genome, this made alignment to the index far faster.

Assembly is when you have no reference, and use the overlap of the reads to build large contigs.  For a while De Brujin graphs were a popular algorithm for that.