Alignment should be used when you are wanting to determine the homology between a set of sequences that span the same gene or genomic region. This function aims to minimize gaps and maximise the overall homology between sequences. Thus, alignment is not appropriate for assembling short sequences into one longer sequence, or for aligning sets of primers into a longer sequence as it will try to put all the sequences on top of each other to minimize gaps in the alignment and is likely to produce an incorrect result.
Assembly is the correct function to use when you wish to merge overlapping fragments of a DNA sequence into a longer contig. This can also be done using a known reference sequence to assist the assembly (Map to Reference), or without a reference sequence (De novo assembly). De novo assembly is generally more computationally intensive than Map to Reference and can require large amounts of RAM.