It is a matter of convention, which may evolve over time and context, including who you are communicate to.
A strict application of the definition of «hydrocarbons» requires that there is at least one atom of carbon plus an other of hydrogen per molecule, and that any atom of the molecule is either of carbon, or hydrogen. However, hydrocarbons like methane (in natural gaz), propane/butane (for camping and lighters), and isomers of octane (for combustion driven engines) are only a small subset of organic molecules. Much of (one might argue, more) interesting chemistry actually only is possible if hydrogen and carbon atoms are replaced (substituted)* by other atoms. The term paraffin you may encounter for this hydrocarbons actually derives from Latin parum affinis which may be translated as of little relationship (only) and (in chemical terms) of low reactivity.
The terms of «organic» and «inorganic» in chemistry are a bit younger, and still inherit a convened discern that the former traditionally requires a molecule of at least two atoms binding to each other: one of carbon, the other not a carbon atom. (In databases like Beilstein, a few classes like carbonates [e.g., $\ce{CaCO3}$] equally are considered as inorganic, too.) These definitions are old, and coined when (because of lack of e.g., spectroscopic methods) knowledge about chemical constitution and structure if accessible was derived by comparison: how your unknown compound would react in reactions already investigated for known compounds?
Over time, means of structure elucidation (e.g., spectroscopy) and synthetic methods evolved; now, the separation of «organic» and «inorganic» is not as sharp as it was at time of e.g., Liebig and Wöhler (terms like e.g., «organometallic»). As an illustration, in heterocyclic compounds, where atoms other than carbon co-constitute the rings, nitrogen is one of the more frequently seen replacements for carbon:

(Sometimes, molecules are stable enough to be isolated as such [e.g., pentazole], sometimes only as motif within a molecule [e.g., 1,2,4,5-tetrazine].)
Similar to the above line leading up to pentazole, given the context and convention an other example which would not fit the above traditional definition of organic is the motif of the phosphazene ring. However, in modern terms, it is an example of organophosphorus compounds with many examples known (a listing by PubChem):

(edited illustration of an abstract).
*) This replacement of atoms is not a pollution, or contamination. If you use the term «pollution», you assume the simultaneous presence of at least two chemical compounds in a sample.