They both contain both elements, but the point is to sharply alter the emphasis. “Software as a Service” is a reasonable description in the salience model of the mainstream software industry, because it is something that you choose and integrate and use like software, except it just so happens to be a service, coming with various costs like subscription fees and very direct vulnerability to upstream changes, and various benefits like installation and maintenance functions being centralized far away where you don't have to directly manage them.

“Service as a Software Substitute” pushes the ‘service’ part to be the most salient. It depicts something which is fundamentally a service, where ‘substitute’ once more emphasizes that you do not, in fact, have the software itself, even though it is taking the role of software. The FSF considers this very important, because they wish users to be able to copy and modify the software they use, and pseudo-distribution purely as a service does not naturally allow for this. If that is not something you care about, then the emphasis will seem strange, yes.