Most small kids skis are more or less the same, if you line up many kids skis you'll notice the twintips and the 'race' skis often are the exact same shape, just a graphic change. As the skis get a little bigger (the 130cm could fall in here) there starts to be actual 'performance' skis (as well as foam core adult look-a-like skis). Race and park skis will start to be very different, the race skis will be built like the adult versions with sidewalls and different SL and GS skis. Park skis will become 'true' twintips, you get wood cores and some structural layers that can stand up to real park use (read: abuse). For a very good kid skier a 'race' ski or a 'park' ski that is built like an adult ski are the best performance options. Very small and light kids don't need a beefy 'adult light' ski, the foam core cap skis aren't bad, bigger or really skilled kids can benefit from the 'better' skis.
When you start to look you'll notice some kids twintips will be $119 and some will be $229... guess which is which.