I am wondering if SDRs (software defined radios), e.g. HackRF, RTL-SDR, or USRPs, are, in essence, just oscilloscopes you can plug to a computer to get the data from it. If not, what are the main differences between such devices ?
All the three devices you mention have mixers, so that's what you wouldn't find in an oscilloscope usually. The amplifiers are optimized for weaker signals, and typically, the quality of ADCs in expensive oscilloscopes is higher than in SDRs – because if you're limited by noise and interference, a high-resolution ADC has very limited benefit.
Also, (higher-end) oscilloscopes are (often) optimized for very high sampling rates streamed into finite-sized memory for display, whereas SDRs are meant to stream continuously.
An SDR is a radio device, an oscilloscope a measurement device.
You can build one out of certain members of the of the other class – the technical difference between the acquisition stage in an oscilloscope and a direct-sampling SDR might not be that large on paper – but clearly, the things that make these devices what they are are not just the ADC!
That depends on how much your definition of "just an oscilloscope" limits functionality. There's probably enough hardware in a high-end O-scope to make at least a receive-side SDR.
The big difference: An oscilloscope lets you see a waveform. A basic oscilloscope just needs to collect a series of samples and display a graph. A basic oscilloscope also gathers information at the same rate that it presents it, but might narrow down the information saved by only acquiring a chuck of it in time.
On the other hand, a radio takes RF, and processes it into something informative (data, voice, pictures, whatever), or it takes something informative and turns it into RF. A radio receiver generally has intermediate steps where it narrows down the frequency spectrum of the received content, but does not take chunks in time.
The biggest difference is that SDR is more of a spectrum analyzer where multiple transmitters can be decoded simultaneously. Scopes are for time domain whereas spectrum analyzers are for the frequency domain.
Also SDR has band switched input filters to minimize front end overloading and getting a much better SNR for the weaker signals of interest, you just cant do that with a scope unless it has a spectrum package built in (in which case its a spectrum analyzer!).
I use SDR for pre-testing in EMC work but I would never use a scope connected to an antenna, that would be silly.