It might be best to tailor your SoP for each school. If you are especially interested in focus X, and a school has many classes on X or they are know for X, then mention it. If another school values a generalist approach, then tailor your SoP to show how you understand that value.
Mention your specific interest in the context of wanting to absorb all you can about your chosen field. You're right that a master's SoP requires less focus -- the MA/MS is about bringing you deeper into the field. It's great if you are particularly interested in X (it shows advanced knowledge and commitment to your field), but show that you are also are eager to learn all they offer in the program. It is the PhD applicants who need to flush out one specific area of interest and why they want to pursue it.
Start with looking again at each school you chose to apply to, and ask yourself these questions before you tailor the SoP for them -- what does that particular program value? (interdisciplinary? field work?) makes makes that program unique? what are they known for? what classes do they offer that you are most excited about? do they have unique aspects (connections with a certain research center, resources for field work, etc.)?