Babies
move plenty before the fourth month. In fact, moms who have been pregnant before can often feel the movements as early as 10-12 weeks. First-time moms are unlikely to detect these veeery faint movements as distinct from gas or other non-baby internal sensations until they get stronger -- about 18-20 weeks or so.
I'm pretty sure the difference has more to do with muscle development and increasing limb size than nerve development.