The results of your primer searches are different using different soft because they use different algorithms. There are better and worse programs to do so but always be careful to check your primers additionally for specificity (use BLAST) and quality (check the possibility of primer-dimers formation - especially for multiplex).
When you do multiplex you'll need to check whether the mixture of the primers amplify only your target sequences or maybe some unspecific as well. This is much easier (a lot easier
) if the genome of the organisms you're working on has already been sequenced and is present in databases [this is likely the case with S.aureus]. Well, it sometimes happens that when you try your primers, despite their carefull selection, you'll have to redesign them. Fortunately the primers are not very expensive.