SMPS is basically a power regenerator.
I'm sorry this is not a correct statement.
You take in the AC & convert it to a high(ish) ripple DC & then feed that into a SMPS & you get a tightly regulated DC power supply.
For a linear power supply you do exactly the same - You take in the AC & convert it to a high(ish) ripple DC & then feed that into a LPS & you get a tightly regulated DC power supply.
So, if SMPS is a power regenerator then so is the LPS.
A SMPS is a DC-DC converter (& so is the LPS).
When you speak of a power regenerator then you take in the AC from the wall outlet, convert it to DC & convert it back to AC (say, like the PS Audio P300/P600/P1200 power regenerators).