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Take for example octahydropentalene (bicyclo[3,3,0]octane) and spiro(3.4)octane:

bicyclo[3,3,0]octane spiro(3.4)octane

I would think that they are chain isomers of sort but according to nomenclature counting rules, they are both 8-carbon main-chains.

However they could also be considered ring-chain isomers but I thought that is only classified satisfactorily by a main chain being closed and open.

I wouldn't think they are functional isomers although it may be true. Since alkadienes and alkynes (this is also a bit grey to me since I couldn't find a good source for it) are considered functional isomers.

Also I would appreciate any primary source that determines the type of isomers two compounds are called and the rules which determine their relation.

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I don't think there is a "primary source" for types of isomerism. The types of isomerism are human-defined categories that different authors find conceptually or pedagogically useful in different ways. It isn't like isomerism classification emerges from some unsupervised analysis of all possible structures.

If it were my opinion, I'd follow the lead of the Master Organic Chemistry web site and call these "constitutional isomers". They have different connectivities: the left structure has two tertiary and no quaternary carbons, while the right structure has no tertiary and a single quaternary carbon.

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  • $\begingroup$ So I take that you mean there is no official further classification of structural isomers( another way to call constituent isomers)? $\endgroup$
    – napstablook
    Jun 30, 2021 at 4:38
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    $\begingroup$ Also according to wikipedia functional isomers is a classification. Would you consider these two functional groups? (Ex. Alkynes and Alkadienes are classified as functional isomers but I couldn't find a good source for it) $\endgroup$
    – napstablook
    Jun 30, 2021 at 4:54
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    $\begingroup$ If you go by the Gold Book, then there is plain old isomer: One of several species (or molecular entities ) that have the same atomic composition (molecular formula) but different line formulae or different stereochemical formulae and hence different physical and/or chemical properties. || And then there are only a hand full of special definitions, i.e. which are widely adapted, e.g. constitutional i., stereoi., tautomers. These are well-defined, but something like functional i. is very dependent on the author. @napstablook $\endgroup$
    – Martin - マーチン ♦
    Jul 4, 2021 at 15:55

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