Normally when thinking about Fluorescence one only deals with visible light, but is it fair to say that the thermal EMR (heat) that's generated from a light source is also a fluorescent effect? For instance, If I shine a high intensity green laser at black tape, it will certainly add more energy into the system which puts the electrons into a higher energy state and emit infrared EMR. Is this correct or am I confusing two things?
Thermal radiation isn't fluorescence simply by definition. It's just blackbody radiation that's related to the object emitting statistically.
There doesn't need to be any electron levels at energies observed. For example most (undoped) dielectric crystals don't have any electron levels in far infrared but will still emit when heated. That's just totally different kind of a a beast.
Here is a blog entry by Chad Orzel I recently read entitled "Things I’ve Never Quite Understood: Microscopic Picture of Blackbody Radiation" somewhat relevant to your question. From comments in this blog entry I took out a reference to a rather interesting paper DOI 10.1119/1.1819931 which can be found here. This however may be behind a paywall for you.
Researchers in this paper show how absorption and re-emission when it happens long enough causes sharp atomic lines observed in gases to vanish, producing continuous thermal radiation. It's just statistical property that doesn't depend on material considered. And yes - it's somewhat confusing even to physicists.