What are the differences between SLRs and DSLRs? (I know that DSLRs are Digital SLRs but are there any actual differences?)
Also, what are the advantages/disadvantages of both?
Nowadays, both terms are using interchangeably because the vast majority of SLRs in production are digital and there was not been a new model of another type of SLR in years.
SLR refers to a camera with a Single Lens and a Reflex mirror to bend the light path to the optical viewfinder for framing. A DSLR is a Digital SLR, meaning it has a digital sensor to record images.
Digital SLRs have may advantages compared to their film counter-parts. You get the digital workflow with instead previews and low usage costs. Taking thousands of images is easy with a digital. On the other hand, each roll of film costs money takes space and most be properly kept until developed (and after too).
Film SLRs have advantages and can be far more durable and resistant to extreme environments. They require much less care and batteries last for years. Some do not even need batteries to operate, although you loose metering and autofocus obviously. They are not prone to sensor-dust (or film-dust) because a new frame is used for each shot.
Advances mean that image quality greatly favors digital cameras which now have over 14 stops of dynamic-range and reach stellar ISO sensitivities as high as 204,800. With resolutions reaching 36 MP too, they can capture a tremendous amount of details.
When DSLRs had around 6 MP people would argue which one captures more details but I have not seen anyone argue about it anymore. Of course, with a film camera, it depends on the film used and the resolution is actually not a uniform grid, so highlights get more resolution and shadows less.
DSLRs are a subset of SLRs.
In other words all DSLRs are also SLRs, but not all SLRs are DSLRs.
SLR is an abbreviation for Single Lens Reflex. What this means is that composition of the scene, focusing, and actually recording the image are all done trough the same lens. The word reflex relates to the way a mirror is used to view the scene and focus it through the viewfinder or a focusing arrray and the way it is flipped up out of the way fractions of a second before the image is recorded. An SLR may use either film or a digital sensor as the recording medium.
DSLR means Digital Single Lens Reflex and inlcudes only SLRs that record the image with a digital sensor.
There are also some mirrorless and translucent mirrored interchangeable lens digital cameras that can be used much like a DSLR. The translucent mirrors do not move (or reflex). Instead they only reflect a fraction of the light to the viewfinder and the rest is allowed to pass through to the lens. Most mirrorless interchangeable lens cameras use the main image sensor for composing the scene and focusing as well as recording the image. Many still have some form of mechanical shutters, many others do not.
Digital Sensors and Film are two distinct recording mediums which both display unique characteristics when recording an image. The way an image is processed, or edited for viewing, is also much different. Both have characteristics that can sometimes be an advantage and sometimes be a disadvantage depending on the subject matter and the qualities the photographer wishes the final image to display. In the end it is a matter of personal taste. For more on film vs. digital please see this question, this question, and this one.
SLR = Single Lens Reflex. Before digital there was only film, so it wasn't qualified as such. Today SLR would tend to refer to film.
DSLR = digital Single Lens Reflex
There are of course improvements overall in latest models, most of which are digital, but there is really no big difference other than the obvious digital sensor instead of film
Advantages for film (at least in the early days of digital)
Advantages for digital