The smaller manufacturers that only put out high-end balls like Morich, Lane 1, Lane Masters, 900 Global, and such, if they make a 12# or 13# version, it's gonna have a core in it. Others, sometimes yes, sometimes no. It can vary from ball to ball.
Some lightweight balls have a different core in them. Storm used to make X-factors with a lightbulb core in the 12-13# versions and the asymmetric RAD core in the 14-16# versions. Track used to do the same thing 12-13# versions would have the core from the Crunch Time while the heavier balls had the big strong asymmetric core.
Brunswick actually puts the same core shape into the lighter weights. They have a file on their website that shows the core shapes and numbers for all weights.
The quick-and-dirty way to know if there's a change in core or core shape is to look at the numbers. While they'll vary some from 14-16#, for the most part, if it's a low-RG, high-diff core, they'll all be low-RG and high-diff. But when you drop to 13#, the diff drops from 0.050" to something like 0.020" and the RG increases from 2.51" to 2.66". That usually means there's a pancake core of some sort that's been substituted.
Finally, most entry-level balls use the same core in all weights down to 12#.
SH