It varies from company to company and ball to ball. That information is usually on the website for a particular ball. Brunswick seems to make a lot of 13# balls with the same core as the heavier weights. Storm is hit-and-miss, sometimes they use lighter weight cores for lighter balls. Track usually uses a different core for 12-13# balls, but it is a "real" core, the same one used in the Crunch Time, Slash, and Solutions. Some Lane 1 balls are available in 13#, some aren't. I can't see Lane 1 using a different core for lighter balls, they seem to simply not make them in that case.
In the end, you have to look at the specific ball you're interested in to find out for sure.
SH