Here we have a basic diagram of a masonry chimney attached to a fireplace. While each individual chimney may vary slightly, this is a good overview of the parts/names of the different areas of a masonry chimney.
Here you can see that masonry chimney structure with a woodstove insert installed.
This is a picture of a fireplace insert, pulled out of the fireplace. Depending on an individual's set-up we may pull out the insert in perform your chimney sweep and inspection.
This diagram show the two set-ups typically used to install a free-standing wood stove.
Here we see a stock photo of a free-standing woodstove, which is attached to a thimble going through the wall.
This is a diagram of a factory-built fireplace. You may also hear this called a pre-fab fireplace. These are fireplaces that are factory manufactured and installed in wood-framed chimney with siding.