Hello Jonte,
Without knowing all the technical differences that the Zorin team implemented between Lite and Core, I would say that you can run the same programs on either. Both versions are based on Ubuntu 20.04 LTS, which itself is based on Debian. This base determines what programs can and cannot run.
On the download page you can see an overview of the differences. The big difference is the use of GNOME or XFCE as the desktop environment (think user interface). These do not affect which programs you can run.
There is one caveat however. As you may notice Zorin Connect does not work in Lite. This is because it is a GNOME specific desktop extension. GNOME and XFCE support different widgets, tweaks and extensions. These affect how the desktop looks, how you can use it, and some information it shows to the user (like weather, resource usage, etc).
Software and games work the same on both. Arguably on Lite, programs will run faster and appear more responsive (hence Lite), while on Core they look better with more fancy animations.
