Both SSAT and TABS
have standard recommendation forms available that can be used for English, Math, and head of school (or guidance counselor) recommendations. They're virtually identical. It doesn't matter which you use. Just print out the form, give it to the teacher, ask him or her to fill it in, make multiple copies, and then sign each copy separately.
Don't overcomplicate things. Some schools have their own online recommendation forms, others have their own printed forms . . . and none of it matters. Any standard recommendation form will do for any school.
As for the application itself, some schools accept both the TABS application, and/or the SSAT application, in addition to their own. Some schools don't. Once you know which schools your student will be applying to, figure out which application forms you want to use. Using one of the two standard applications will make your lives easier (and the two are virtually identical), so feel free to submit one of those if the school says it's okay.
The key difference between TABS and SSAT, by the way, is that SSAT is, as you suggested, an actual service. You submit the stuff online, SSAT then processes it and sends it on to the schools(s). TABS simply has a collection of application/recommendation forms that you print out, fill in, and submit to the schools yourself. Unless your student is applying to a school that actually requires one or the other (such as Lawrenceville, for example, which accepts ONLY the SSAT application), just pick the one you prefer.