When you define a base of vectors, in your case $\{ |1,1\rangle, |1,0\rangle, |0,1\rangle, |0,0\rangle \} $ you assign to each vector some phase, e.g. the vector $|1,1\rangle$ has a certain phase that you don't mention explicitly outside the bra-kets. Now, in your calculi you may have superpositions of these vectors of the form
$|\psi\rangle = ae^{i\alpha} |1,1\rangle + be^{i\beta}|1,0\rangle + ce^{i\gamma}|0,1\rangle + de^{i\delta}|0,0\rangle,$
with $a, b, c, d$ positive numbers, i.e. besides the intrinsic phases of the four vectors, they appear in the superposition with complex amplitudes. Thus the amplitude of $|0,0\rangle$ has a difference of phase in comparison with the amplitude of $|1,1\rangle$ and this difference is $\delta - \alpha$.
Returning to your functions, in the first superposition the vectors $|1,1\rangle$ and $|0,0\rangle$ are in phase, while in the 2nd superposition they are in anti-phase, there is a difference $\delta - \alpha = \pi$ between them, i.e. you can write
$ \frac {1}{\sqrt{2}}e^{i \cdot 0} |1,1\rangle + \frac {1}{\sqrt{2}}e^{i\pi}|0,0\rangle$
.