"Two molecules that have the same chemical formula, and
have the atoms connected together in the same way but still be
different" refer to stereoisomers, rather than structural
isomers.
(Note however, the question "still be different" is
vague. Depending on other factors, two molecules in
different microenvironments, different temperatures, different
pressures, different inter-particulate forces or energies acting on
them, will naturally have different energy levels and hence
"still be different" even if they are actually identical and
not stereoisomers.)
Isomers are divided into structural aka constitutional isomers,
and stereoisomers.
Structural isomers are subdivided into chain
isomers, positional isomers, and functional group isomers.
Stereoisomers are subdivided into geometric (Cis-Trans or E-Z)
isomers, and optical (Dextrorotatory-Levorotatory or
Rectus-Sinister)
For more information, google (it is now officially an English
word) "isomers" on Wikipedia or Answers.com