The most common smoke issues are weak injection pump, worn injector tips, incorrect pump timing, head gasket failure. Not necessarily in that order.
The fact you have smoke from one side of the engine says it isn't likely a seal of any sort. My 83 pick-up always was smoke free within 5 seconds of cold start...until this summer when for no apparent reason I started getting a goodish amount of blueish/white smoke from the passenger pipe at start-up, and continuing on for much longer than previously.
I swapped out the 4 passenger injectors with known good spares I had. No difference. The IP had been rebuilt a few years ago so wasn't on my list of probably causes.
Then it hydro-locked on me once when it had been run to warm, shut off and attempted to re-start 5 minutes later. For me it was head gaskets, or more accurately the TTY (Torque to yield) head bolts loosing their grip. My suspicion is that the head bolts had just a tick too much torque on em and eventually stretched a bit more. When I was pulling the heads there were four head bolts that didn't seem tight at all.
I replaced the head gaskets and added ARP screw in head studs...tis all good now.
On my K5 I started getting significant smoke at start-up that wouldn't quite ever go away. It got progressively worse and worse. I sent my IP and injectors out for rebuild, and after getting it back together it hardly smokes at all during cold start, and clears up very quickly after. This is on a motor with 240,000 miles on it...
The injector tips when they wear out allow the fuel to drip and glob out of them rather than the micro-fine mist they're supposed to deliver. The globs and droplets don't ignite and burn properly, and can cause smoke.
Rene