Note that usually electrons are somewhat localised, and that localisation is part of the quantum state. The Pauli principle is a consequence of the symmetrization postulate, that states that, for fermionic particles, the wavefunction must be antysymmetric if you exchange the coordinates of any two particles. A common example is that of two electrons in the same atom, with quantum numbers $n, \ell, m_\ell, s$ and $n', \ell', m_\ell', s'$. The antysymmetrized wavefunction is (assuming that the electrons don't interact): $$\Psi(\vec{x}1, \vec{x}_2) = \frac{1}{\sqrt{2}}\left[\psi{n\ell m_\ell s}(\vec{x}1)\psi{n'\ell' m_\ell' s'}(\vec{x}2)-\psi{n\ell m_\ell s}(\vec{x}2)\psi{n'\ell' m_\ell' s'}(\vec{x}1)\right]$$ where $\psi{n\ell m_\ell s}(\vec{x})$ is the wavefunction for one single electron in the atom. 976
It's easy to check that if you set $n=n'$, $\ell = \ell'$, $m_\ell = m_\ell'$ and $s=s'$, you get $\Psi =0$, so you can't have a wave function for two electrons with the same quantum numbers.
The situation is different if you have electrons in two different atoms, one of them centered at $\vec{x}=0$ and the other centered at $\vec{x} = \vec{x}0$. The wavefunction for this system is $$\Psi(x_1, x_2) = \frac{1}{\sqrt{2}}\left[\psi{n\ell m_\ell s}(\vec{x}1)\psi{n'\ell' m_\ell' s'}(\vec{x}2-\vec{x}_0)-\psi{n\ell m_\ell s}(\vec{x}2)\psi{n'\ell' m_\ell' s'}(\vec{x}_1-\vec{x}_0)\right]$$ In general, this wavefunction won't be zero even when all the quantum numbers are the same for both electrons.
In principle, the Pauli principle applies to all electrons, as they are excitations of the same fermionic field. But in practice, it has little effect (or not effect at all) when you consider two particles that are far away.
Imagine that you have an electron with wavefunction $\psi(x)$ and other with wavefunction $\phi(x)$, and that both electrons aren't interacting. If you could distinguish both electrons, the colective wavefunction would be $$\chi(x_1, x_2) = \psi(x_1) \phi(x_2)$$ but since the electrons are indistinguishable, and the state must be antisymmetric in the coordinates of both particles, the correct wavefunction is $$\Phi(x_1, x_2) = \frac{1}{\sqrt{2}}\left[ \psi(x_1)\phi(x_2) - \psi(x_2)\phi(x_1)\right]$$ The wavefunctions of both electrons are localised in different regions of space $D_\psi$ and $D_\phi$: $$\psi(x) = 0 \textrm{ if }x\not\in D_\psi \qquad\qquad \phi(x)=0 \textrm{ if } x \not\in D_\phi$$ If the distance between the electrons is large, $D_\psi \cap D_\phi = \emptyset$, and therefore their wavefunctions don't overlap.
We have a measurement device $A$ which operates only in region $D_\psi$ and another measurement device $B$ that operates in $D_\phi$. They have eienstates $a(x)$ and $b(x)$, respectively. 976