The popping and pinging is due to the wheel builder having left residual wind-up ("twist") in the spokes as he was bringing the wheel up to tension. When the wheel is cyclically loaded, the slight relaxation in tension of the bottom spoke allows it to untwist in the nipple and loosen permanently (well, until you tighten it again.) The proper procedure while tensioning is to twist every spoke nipple a quarter to a third turn beyond where you want it, then back off the same amount. The spoke should now be tight but not twisted. As a test, you press down on the rim in several places with the axle end resting on the floor. If you have built the wheel properly you will not hear any pings, nor when you ride it the first time. If you do hear pings, you need to retrue and retension the spokes that pinged (in practice you go around the whole wheel), paying more attention to eliminating wind-up this time.

Stress-relieving is a separate operation that is unrelated to spoke windup. Stress-relieving doesn't make any noises. It can't relieve residual twist because the operation momentarily over-tightens the spoke; twist is relieved only when the spoke slackens. Before you do the stress-relieving, you want to have already removed residual wndup. A wheel that has not been stress-relieved will not ping when ridden, but it will break spokes sooner. Good wheels need to be twist-eliminated and stress-relieved.

(I emphasize that I am talking only about traditional wire-spoked wheels of 28 spokes or more. I know nothing about low-spoke-count wheels.)

Interesting that purchasers of machine-built wheels often find it necessary to retension them. I wonder if the value of their time makes it actually more cost-effective to build their own from scratch even though the retail cost of the components exceeds that of the complete wheel....?