Here's a nicely simplified description of the structure of coal:
V.D Macromolecular Nature of CoalsCoals are believed to be three-dimensionally cross-linked macromolecularnetworks containing dissolved organic material that can be removed by extraction.This model offers the most detailed and complete explanation of the chemical andmechanical behavior of coals. It is a relatively recent model and is somewhatcontroversial at this writing. The insoluble portion of the coal comprises thecross-linked network, one extraordinarily large molecule linked in a three-dimensional array. This network is held together by covalent bonds and hydrogenbonds, the weak interactions that play such a large role in the association ofbiological molecules. The extractable portion of the coal is simply dissolved inthis solid, insoluble framework.
That was taken from a 2003 article in an encyclopedia about coal structure.
The plant matter the coal came from was somewhat similar in nature in that it also contained a lot of cross-linked organic molecules. The above can be read to imply that each lump of coal is a single solid molecule plus dissolved liquids and gasses but that's probably taking it a bit too far.
Lots of chemical reactions happen under heat and pressure including increased cross-linking of organic molecules. The heat and pressure can be viewed as shifting bonds as well as adding them. In the former case, that's still at least somewhat representative of the original sun-energy donation to the cause.
Note that the dissolved organics like methane (natural gas) are probably a mix of decomposed plant material and compounds produced under that same heat and pressure. If you want to get a sense of what those are, read up on making coke from coal for use in steel making.