Molecules with the same empirical formula but different structures are called isomers. Isomers are quite common in carbon based molecules; which can form simple single chains, chains with side branches, or ring sturctures. These would all have different properties even if the formula was the same for each.
In general, the term "isomer" is used to describe two molecules with different structures and the same molecular formula. However,there are a variety of supplemental terms used, depending on the type of dissimilarity between the two molecules.
1. Structural or constitutional isomers refer to two compounds of different types. For example, the formula C2H6O could be ethanol (C2H5OH) or methyl ether (CH3OCH3).
2. In compounds where there is a double bond present, there can be geometric isomers. They have the same structure, but one molecule has two groups on the same side of the double bond while the other molecule has the two groups on opposite sides of the double bond. These are denoted as "cis" or "trans" isomers.
3. Two molecules with identical structures may exist as mirror images of each others. If this is true, they are referred to as "enantiomers".
4. Some molecules, without a double bond, may have different 3-D shapes or arrangements and these are referred to as "diastereomers".