What is the difference between structural isomers and stereoisomers?

Structural isomers have the same molecular formula but a different bonding arrangement, or connectivity, between these atoms. This leads to different physical and chemical properties between stereoisomers. 

An example of stereoisomers would be 2 possible forms of C₄H₁₀ as 2-methylpropane (or isobutane) and butane.
 

Stereoisomers also have identical molecular formulae BUT the arrangement of their atoms is also identical.
Stereoisomers only differ in the 3D spatial orientation of the groups in the molecule.

The simplest type of stereoisomerism is cis/trans isomerism. Where the restriction of bond rotation due to the presence of a double bond/ ring system leads to the possiblity of cis and trans forms. 

For example but-2-ene (C₄H₈) can exist as cis or trans.