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:
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)
Gallery - A selection of things displayed usually in a either a Pintrest type way or as a series that you step through.
Carousel - is a revolving selection of things that are either automatic or user input driven or at a fair ground.
Slider - is a control element usually seen in things like music/video apps (seek bar) or as a volume control that a user drags or selects at an arbitrary point. Sliders are useful for allowing a user to tweak values in an intuitive way.
Over time there has been overlap of the terminology which appears to have come from the animation used in popular carousels (the slide left/right).
The clear distinction between "slider" and "carousel" lies on the user experience that both deliver, which define the context of both words:
- Slider --> a knob or lever that is moved horizontally or vertically to control a variable.
- Carousel --> a merry-go-round.
Personally, I would opt to address, articulate and deliver them "distinctively"! I would stick to Andrew's perspective! ;o)