Is there a real difference between eternal inflation and "chaotic inflation" theories?
So the 'old' model of inflation was based on the idea that a scalar field (the inflaton) was trapped initially in some meta-stable vacuum. If it's energy density dominates the Universe at this time then the Universe inflates. This continues until the field tunnels out of this vacuum and inflation ends. This leads to bubble nucleation as different patches of the Universe tunnel into the stable state at different times and expand at the speed of light. Reheating in this model occurs when bubble walls collide, thermalising the latent energy stored in these walls. There were problems with this model as it produced a too inhomogeneous Universe.
The 'new' model of inflation basically proposed the idea that after this tunnelling process the scalar field could still be overdamped and slow rolling thus allowing for inflation to continue. This means that inflation occurs within a single bubble thus our Universe exists within this single bubble. This eradicates the inhomogeneities within our observable Universe and reheating occurs through the coherent oscillations of the scalar field about the true minimum.
Both these models where inspired by a GUT phase transition, which is quite often a first order phase transition due to the fermion and boson content.
'Chaotic' inflation is the idea that we need not have the scalar field initially trapped in some meta-stable vacuum. At the Planck era it is likely that all degrees of freedom have Planckian energies (chaotic initial conditions) and regions in which the potential energy of the inflaton dominates will trigger a period of inflation. This typically requires Planckian field values.
Eternal inflation is a consequence of the inflaton's quantum fluctuations. These fluctuations can kick the inflaton around in it's potential and can indeed drive the inflaton field back up the potential to a higher field value. So inflation will continue indefinitely in some patches. This eternal inflation picture generically results in bubbles of the Universe which are expanding at different (exponential) rates and so most of the volume of the Universe is inflating. This arguably, makes it likely that we find ourselves in a Universe which inflated. This seems to be an unavoidable feature of chaotic models.
I realise that this answer is a little late, but hopefully it helps.