Yeah, the first one is right. Don't worry too much about why you only have

sometimes, but it's got to do with the fact that strong acids will do this to nearly 100% completion:

This means that you
can think of the acid as two ionic species, because the covalent molecule isn't even there anymore.
Reactions that ignore the conjugate base,

do this because they just want to show the interaction of the acidic proton with the other species.
But in a general chemical equation, we want to show this change in chemical state (from covalent to ions), so we technically should include the chlorine atom as part of the hydrochloric acid molecule on the left-hand side (because it was originally that). So we do include this in the ionic equation.