Thuban's pretty well got it. There are two concepts to consider;
i) Where do I get my energy from?
ii) Where do I get my carbon from?
For i) there are 3 options;
a) Chemotrophs get their energy from organic molecules that have been synthesised by other living creatures. These can be pretty simple compounds like acetate or quite complex like baked beans on potatoes.
b) Chemolithotrophs get their energy from inorganic compounds or hydrogen. Commonly energy can be extracted from elemental sulfur, sulfate, sulfide, ammonia, etc. As the name connotes, these bugs can live off of rocks.
c) Phototrophs get their energy from light (not necessarily in the visible spectrum).
For ii) there are 2 options;
a) Heterotrophs get their carbon from organic molecules, regardless of where they get their energy from. Thus, an organism can be a chemolithoheterotroph.
b) Autotrophs 'fix' their carbon from simple sources such as carbon dioxide or carbon monoxide. Thus, an organism could be a chemoautotroph.
Something describes as being photosynthetic strictly speaking means it gets it's energy from light and fixes its carbon, usually, from carbon dioxide. i.e., it is a photoautotroph.
My favourite part conversation word is "chemolithoautotroph".
Then there's "obligate" and "facultative" but I'll leave that for another day.
Last thing to note is that chlorophyl is only one of the photoreceptor pigments that Life uses. It is used by cyanobacteria and in the chloroplasts of plants. Many other chemicals are used by different organisms. So it's better to refer to "photoreceptor pigments".