Ceredigion County council is the principal council for the whole of Ceredigion, including Aberystwyth. For example, it runs schools, collects rubbish, delivers social care, runs car parks and employs traffic wardens, makes planning decisions and so on. It owns the promenade and castle, as well as lots of other things in the town and the rest of the county.
In that sense, no, Aberystwyth Town Council does not do those things. But it is an elected council on a much smaller scale than Ceredigion.
It’s important not to mix these up when talking about “the Council”. They are very different. That is why we want to help people by trying to explain what Aberystwyth Town Council is and what it does.