Yes, you probably can use both bullets in both rifles.
If you are an experienced re-loader, you can make up ammo using either 308 bullets or 312 bullets and shoot them in both. The bullets will be tight in one bore and loose in the other. Accuracy might be ok, or might be very poor.
Before loading the 312s in the 3006 brass, stick a bullet into the case mouth of a fired 3006 case. If it fits in with no resistance, your rifle has the neck clearance to take the fatter bullet. Seat the fat bullet deep, so it has a running start at the tight throat.
That said, this is not the kind of load development a noob should try.
Buy a box of 308 bullets and a box of 312 (or 311) bullets. I suggest 180 gr flat base (lead core) bullets to start with.