Is the first circuit a real circuit (minus the component values), or is a 'conceptual' circuit?
That is, could some values be added to the circuit components, and that is all that is needed to be done?
I'd call it "conceptual, but. . ."
. All the major players are there, but without specifying the 3-terminal regulator it's impossible to say. For instance, 78xx regulators like to have a couple of caps on them to handle transients and prevent oscillation. Others may have other requirements.
Plus, I'd really want to put a fuse on it, and a switch, and a cap on the AC side (but I'm a bit fuzzy on that bit since you'd need to calculate it to avoid resonance with the transformer, or so I'm told).
That said, if you pulled off the regulator, it's essentially what you'll find inside a wall wart. So in that sense, yes, it's a complete linear power supply schematic, but it needs a few more bits to make it a decent one.
My usual disclaimer: I'm a hobbyist (read: just some yahoo with a soldering iron). If I'm leading you down the garden path I hope to be corrected by one of our resident experts. But I have built a few linear supplies. The early ones resembled the first schematic shown here. And all of them contain at least those stages (stepdown transformer, rectification, filtering, regulation).
It really depends on what you need it to do and what sort of specs and performance you want to see out of it.
Torben