This
{ts[112,3], ts2[112,3]}
shows that the form of the two expressions are different.
This
FullSimplify[ts[112,3]==ts2[112,3]]
shows that the two expressions are exactly equal if you are using exact math at every step.
Turning ts and ts2 into numerical approximations requires working through the parts of each expression one step at a time and turning those into approximate MachinePrecision numerical expressions. During that is where slight differences in approximate math show different approximate results that you are seeing.
I suspect exactly the same is the cause of what you are seeing for z3b1 and z3b2, but I didn't wait long enough to see the final result of summing those from zero to Infinity.