How offset current and offset voltage affect output of single-ended diff amp?
The output of singled-ended diff amp is referenced to ground so that
if one side of diff amp is in offset compared to the other side

That's incorrect. The output of an op-amp is: -
$$A_0\cdot(V_{IN+} - V_{IN-})$$

\$A_0\$ is open-loop gain
\$V_{IN-}\$ is inverting input voltage
\$V_{IN+}\$ is non-inverting input voltage

And, it is how you implement the feedback and connect the input pins (\$V_{IN-}\$ and \$V_{IN+}\$) that determines where the output voltage is referenced. In the below example the output is referenced to ground by virtue of \$R_G\$ but it needn't be - the bottom connection of \$R_G\$ can go to any reasonable voltage within the positive and negative supply rails of the op-amp: -

So now you can see that \$V_{OS}\$ can add or subtract from the input signal and the output error will be \$V_{OS}\$ multiplied by the closed-loop gain.