What we usually call “an RSS reader” is supposed to basically do two things: check the feeds to get what’s new and organize it in categories or otherwise (this part is actually properly called an RSS aggregator), and then give you the interface to actually read it (the RSS reader proper).

Aggregators usually include a reader, but some don’t, and doing one thing good (aggregating or reading) is easier than doing both good, so a decent aggregator usually supports using your own reader.