Page 564 of the Core Rulebook describes paralysis as the following...
"Some monsters and spells have the supernatural or spell like ability to paralyze their victims, immobilizing them through magical means. Paralysis from poison is discussed in the Afflictions section. A paralyzed character cannot move, speak, or take any physical action. He is rooted to the spot, frozen and helpless. Not even friends can move his limbs. He may take purely mental actions, such as casting a spell with no components. A winged creature flying in the air at the time that it becomes paralyzed cannot f lap its wings and falls. A swimmer can’t swim and may drown."
These are what the following conditions say...
Paralyzed: A paralyzed character is frozen in place and unable to move or act. A paralyzed character has effective Dexterity and Strength scores of 0 and is helpless, but can take purely mental actions. A winged creature f lying in the air at the time that it becomes paralyzed cannot flap its wings and falls. A paralyzed swimmer can’t swim and may drown. A creature can move through a space occupied by a paralyzed creature—ally or not. Each square occupied by a paralyzed creature, however, counts as 2 squares to move through.
Prone: The character is lying on the ground. A prone attacker has a –4 penalty on melee attack rolls and cannot use a ranged weapon (except for a crossbow). A prone defender gains a +4 bonus to Armor Class against ranged attacks, but takes a –4 penalty to AC against melee attacks. Standing up is a move-equivalent action that provokes an attack of opportunity.
As you can see the two are quite different, a prone PC can get back up. A paralyzed PC is more or less frozen. I hope this helped
