How similar or different are the magnetic field patterns produced by two bar magnets when; a.) like poles are facing each other? b.)when unlike poles are facing each other?
The two field patterns are completely different, but still share similarities (the “rules” of field lines still apply.)
Firstly, the second point: field lines never cross, each have an arrow to show the direction of the field (a vector) at that point (conventionally drawn going from a north and into a south pole) and finally they stretch out to infinity (but we never have the required patience to draw them all.)
OK, now to your question. When two like poles are pointing towards each other the field lines ‘splay out’ and when dissimilar poles point towards each other they are ‘sucked in’ thus:
One final point - you can always derive the direction of the forces in play if you remember that field lines tend to straighten and shorten.