So this may be an incorrect assumption, but from my knowledge solar systems are heliocentric and there are always suns. (I realize to be a solar system there must be a sun semantically.) But it seems to me that planets and stars are just bodies of mass, so are there cases of solar systems where the star is just one of the bodies of the system and orbits around a super massive planet? And similarly are there 'solar systems' without stars, where there are a group of planets orbiting a massive planet at the center of the system?
Generally, astronomical bodies rotate around their common center of mass, not the one or the other body.
If one of the bodies is much heavier, the center of mass is much nearer to its center, sometimes even inside the larger body. For example, Earth and Sun both rotate around a point that is much nearer to the Sun's center than to the Earth's center, as the sun is much heavier. Looking from the outside, it seems as Earth rotates around the Sun, while the Sun just wobbles a bit in sync. But the reason for that is exclusively the masses of the bodies, not their being-a-star or not-being-a-star.
Your theoretical example of a super-heavy planet and a lighter star would result in the star seemingly rotating around the planet; however, here you need to look at why a star is a star:
Stars are created by gravity that is compressing the mass to a level that starts fusion, and thereby a star. In your example, either the 'light star' wouldn't make it into a star (and be a light body/planet), or the 'super-heavy planet' becoming a much brighter star (or both of it). That reverses the roles effectively.
Looking at it this way, the bodies in a system rotate always around the center of the mass, which is near the largest mass, which will be the first star of the system (if any).
So your first constellation is not possible.
The second is well possible - if neither of the bodies has enough mass to become a star, they will be still rotating around each other the same way, with the heaviest body being nearest the center. Such a system would be dark and basically invisible from some distance. We wouldn't be able to find them.
From my knowledge solar systems are heliocentric and there are always suns. (I realize to be a solar system there must be a sun semantically.)
Just a semantic note, systems of stars and planets different from our own are referred to as stellar systems. The solar system refers specifically to our own stellar system since solar means "of or relating to our own Sun".
To remark on this point though, yes this is (somewhat) true. All stellar systems are heliocentric in that all bodies orbit the central star (or stars) of that system.
What is technically more true is that all systems are barycentric, in that all bodies (including the star) orbit the common center of mass, known as the barycenter. It just so happens that the star tends to have $>99\%$ of the mass of any stellar system and so the barycenter is very very close to the center of the star. Our own Sun does actually have a measurable orbit around this barycenter.
Where it gets really interesting is when you have a stellar system with more than one star. In this case, the barycenter is no longer near the center of any particular star and so you have noticeable orbits of the stars.
But it seems to me that planets and stars are just bodies of mass, so are there cases of solar systems where the star is just one of the bodies of the system and orbits around a super massive planet?
As stated above, all bodies orbit the barycenter. The location of the barycenter depends on the masses of all the bodies in the system and will be closest to the most massive body. Think of the barycenter as a weighted mean of the positions of all the bodies, where the weight is the respective body's mass (because that's exactly what it is). That's just how the math works out. It is impossible then for the objects in a stellar system to orbit a less massive body as the barycenter could never be closest to that body.
And similarly are there 'solar systems' without stars, where there are a group of planets orbiting a massive planet at the center of the system?
The only possible case would be a system which doesn't technically have a star. It is quite possible that a system might try to form but just not have enough matter to get very big. The central object would try to become a star, but might not actually be big enough to start shining. We call these objects brown dwarfs. There are almost assuredly systems which have no official stars and the central body is a brown dwarf that every other body in the system orbits around. Whether you want to consider this brown dwarf a "massive planet" is a bit hazy.