Originally, they were all DNI, but then the entire 'DNI' thing became something of a shortcut for 'I can deck through this', and frankly, you shouldn't be decking (or being able to be hacked) by way of someone's cyberarm, so ...
If you like, a standard neural interface (SNI) is akin to a baseline nervous system, as appropriate for the piece of ware you have. Like Kiirnodel says, it lets you use your cyberarm like an arm, use a trained 'pseudo-muscle' effort to pop out its spurs, or to try to make an 'impossible hand gesture' to open up the palm-port for your cybergun. It lets your cybereyes focus, lets you 'pinch' certain eye muscles in certain ways to switch overlays, that sort of thing. Or wired reflexes, or (maybe) the switch-over to your rigger wires. Most of these are not actually tied into the standard 'thinking' portion of your brain; they'd work through you trying to do something, or a sequence of somethings, which you can't (or don't) normally do.
Compare this to the direct neural interface (DNI), which instead of patching into the limbic &c. systems, patches into ... I guess your cerebrum and cerebellum? I'm not up-to-date on (or have forgotten) which portions of brain house 'conscious thought'. But that's generally the key -- conscious, intentional thought. That's where you hack from, where you turn your attention from, all that sort of thing.