I was wondering if all modern digital scopes today offer real-time sampling?
Yes, most scopes today are Real-Time Sampling (RTS) scopes. Some also support Equivalent Time Sampling (ETS), but not all of them.
In general, ETS-only scopes are a thing of the past unless you need more than 65GHz bandwidth. Above that there are some older scope designs which go to 100GHz and which are still sold, but these will probably be replaced by RTS scopes soon.
For most digital scopes the sampling rate is divided by the number of active channels.
I guess this is because they perform real-time sampling?
No, not really. Yes, it's RTS, but the reason why on some scopes the max sampling rate is dependent on the number of active channels is because they use interleaving (combining a channel's ADC with the ADC of an inactive channel) to reach higher sampling rates when only one or two channels are active.
What do most digital scopes offer today? Both options?
As I said above, ETS-only scopes are dead outside extremely high bandwidths, and this has been the case for more than 15 years.
Most of the better scopes also offer an ETS mode as well, but not all do. Especially cheaper low end scopes often lack that feature.
Are their other differences in the way digital scopes sample the incoming signal, besides actual sample rate, real-time or equivalent-time sampling?
Like to have a better understanding about the different possible implementations, and how they differ between Tektronix, Agilent, Rigol, etc.
Not really. The basic principle behind RTS scopes is the same. Some use technologies like DBI (Digital Bandwidth Interleaving) where signal components are downmixed, but this is only used in certain highend scopes (i.e. LeCroy's 100GHz RTS scope demonstrator uses DBI).
However, not all ETS implementations are the same. For example LeCroy uses something called RIS which works different than ETS modes of of other manufacturers. This pdf explains RIS and other ETS modes in more detail:
http://cdn.teledynelecroy.com/files/whitepapers/wp_ris_102203.pdfTektronix TLS216: this scope had massive amount of 16 channels, had 2 GS/s per channel, irrespective of how many active channels you were using. How did they do that?
Probably by using a 2GSa/s ADC per channel. Not all scopes use ADC interleaving, as this comes with its own issues when designing a scope.
Philips PM3340: This scope offered 2GS/s back at that time. But it was equivalent-time sampling. Does anybody know if it also offered real-time sampling, and what the actual bandwidth was?
The PM3340 was a 2GHz scope with 250MSa/s real-time sampling rate and
14bit 10bit vertical resolution which also offered 2GSa/s in ETS mode. It was a good scope at it's time (1989; I had a
PM3343 PM3320A back then which was the 200MHz version of the PM3340) but by today's standards it's a boat anchor. It's also difficult to fix with lots of unobtainium parts. The high vertical resolution made (and still makes) especially the
PM3343 PM3320A sought after for audio work, though.
Edit: The scope was a PM3320A not PM3343, and had 10bit vertical resolution not 14bit.