Isomerism due to shifting of proton from one atom to another in a same molecule is known as:
Metamerism is the type of isomerism in which chemical compounds have identical proportions of the same elements and the same molecular weight, but have radicals differing in type or position, with resulting differences in chemical properties.
Tautomerism is the existence of two or more chemical compounds that are capable of facile inter-conversion, in many cases merely exchanging a hydrogen atom between two other atoms, to either of which it forms a covalent bond.
Positional isomers are constitutional isomers with the same carbon skeleton and will have the same functional group. They differ from each other in the position of the functional groups on the carbon chain and the phenomenon is known as positional isomerism.
Functional Isomerism is also known as functional group isomerism. As the name suggests, it refers to the compounds that have the same chemical formula but different functional groups attached to them.
A tautomer of a compound refers to the isomer of the compound which only differs in the position of protons and electrons so, B is correct.
In the rest of the options (A, C, and D), there is a difference in the positioning of whole atoms and not just protons, which is why these options are incorrect.