It's different. Both the spear and the javelin have the thrown property; sling bullets and arrows do not. (Actually, I think the bow and sling should key off Str, not Dex, but that's for another thread.)
The sling, the bow and the spear thrower are all devices - you know what a spear thrower is right?
Spear-thrower - Wikipedia
en.wikipedia.org
a sling is a variant of the same principle, so the same rules should apply.
A sling stone does not have the thrown property. Nor does an arrow.
So if you take a sling stone and throw it with your hand... what happens here?