From a pattern perspective is there a difference? Or are they really different names for the same thing?
Sliders and Carousels effectively they mean the same thing: while perhaps factually different at one time, they are conflated to such a degree today that you couldn't effectively communicate one meaning or the other without being misunderstood. 1) A quick Google survey of jquery "sliders" and "carousels" shows many variations of the same thing: people are using these terms interchangeably as a means to display a "gallery" of photos. 2) The developers in my office respond to the question with "tomayto tomahto."
In the case of Galleries, these are the overall collections of images presented via carousels & sliders. Galleries tend to be presented in grids and lists.
I don't disagree with Andrew's usage (slider=horiz/vert, carousel=rotating focus), per se, but if you want to use terminology that will ensure you are not misunderstood, you might just call everything a carousel, and specify what sort of navigation it uses: filmstrip, slider (although I would avoid that), prev/next or stop/play buttons, dots, etc.
I attach some sketches to illustrate examples of what I mean:
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A slider and carousel are NOT the same thing. A slider slides the images horizontally or vertically (usually horizontally) usually with a momentum effect.
A carousel rotates the images radially and in a 3D feel by using distance and depth of field. They rotate on an axis where the image is always facing you.
A gallery is usually where all images are available to see... but that doesn't mean a slider or carousel can't show all the images either. A gallery is also the umbrella term for anything that shows images... or the name of the page where you see the images. Usually completely filled galleries will be styled in a matrix layout.
The content and inclusion of all or featured images is up to the designer of the application in mind (site, app, etc)