Paired-end alignment typically means keeping track and reporting the alignment of the booth pairs in a read pair.
Each read is aligned separately, and the information on both pairs is combined and reported in the same alignment line.
Basically, this allows other, subsequent analysis tools to infer additional information on the fragment just by reading a single line of the alignment.
In principle, you could take the two pairs, align them in single end mode then postprocess the two single end alignments and generate a paired-end file yourself from the existing information in the single end alignments. But the process would be tedious and wasteful, hence it is better to generate the paired end alignments at the time of the original alignment.