Cisplatin and transplatin are obviously isomers, more precisely stereoisomers. Now, they aren't chiral, so they cannot be enantiomers. They cannot be diastereomers either since they don't have two stereocenters. They don't belong to cis/trans stereomers either since they are a subgroup of diastereomers and again require two stereocenters. So - what the heck?

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    $\begingroup$ Yes they do belong to cis/trans isomers, simply because they are called cis and trans, if not for other reason. True, this is a quite different kind of cis/trans from that known in organic chemistry. Whatever. $\endgroup$ – Ivan Neretin Feb 17 '17 at 18:46

The definition of diastereomer does not include "requires two stereocentres" anywhere. It is simply

Diastereoisomers (or diastereomers) are stereoisomers not related as mirror images. (IUPAC Gold Book)

Therefore cis- and trans-$\ce{[PtCl2(NH3)2]}$ are diastereomers.

(E)- and (Z)-alkenes are also diastereomers of each other. Your "cis/trans stereomer" is in fact simply a subset of diastereomerism.

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