Both attacks, in their practical form, use cache timing as the side-channel to extract information. But the surprise is the control over (as the paper calls them) 'transient executions'.
like check this out: https://www.tau.ac.il/~tromer/acoustic/
> Here, we describe a new acoustic cryptanalysis key extraction attack, applicable to GnuPG's current implementation of RSA. The attack can extract full 4096-bit RSA decryption keys from laptop computers (of various models), within an hour, using the sound generated by the computer during the decryption of some chosen ciphertexts.
So the seriousness of a side-channel attack is determined as a function of the impact of the exploit as well as how easy it is to carry out the exploit.
Meltdown in particular is nasty because it is relatively easy exploit and is undetectable and affects a ridiculously large range of hardware. So it is actually a pretty big deal. Yes there are side-channel attacks against Intel CPU's, but this isn't just any old side-channel attack.
Here's just one of the more practical attacks http://palms.ee.princeton.edu/system/files/SP_vfinal.pdf
>but this isn't just any old side-channel attack.
It isn't, but you were already screwed. Now you're just slightly more screwed.
Not some artificial poc that already knows an address to attack and needs to be helped by continually pulling the data into the L1 cache.
If it is so easy to do then why has nobody written anything that can read a password from a browser or sudo?
But perhaps this was no big deal. We've seen years of research suggesting that modern CPUs are full of issues like this. There's probably a good decade worth of papers on cache side channel attacks. See https://eprint.iacr.org/2013/448.pdf for example
Perhaps the big deal is that there are still people who think they can safely run multiple different things on a single machine?