Which is the correct definition for metamers (or metamerism)?
There is no IUPAC definition for metamers or metamerism in the gold book (not even one that makes it obsolete), and Wikipedia doesn't even have a real article about it, see Metamerism.


  In chemistry, the chemical property of having the same proportion of atomic components in different arrangements (obsolete, replaced with isomer). In organic chemistry, compounds having the same molecular formula but different number of carbon atoms (alkyl groups) on either side of functional group ( i.e., -O-,-S-, -NH-, -C(=O)-) are called metamers and the phenomenon is called metamerism.


I cannot find any authoritative source for this, but there is a question discussing it on our platform: What is metamerism? Also related: Are methyl n-propyl ether and methyl iso-propyl ether metamers?

Any of the two definitions cited in the question match the general definition of isomers.


  isomer (DOI: 10.1351/goldbook.I03289)
  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.


More particularly, they match the definition of constitutional isomers.


  constitutional isomerism (DOI: 10.1351/goldbook.C01285)
  Isomerism between structures differing in constitution and described by different line formulae e.g. $\ce{CH3OCH3}$ and $\ce{CH3CH2OH}$.


Metamers/ metamerism is an archaic, ambiguous, and deprecated term in chemistry. Don't use it.