Exception in odd cases: it you are trying to re-use a SATA HDD from another computer, it MAY have had a special adapter plugged into the normal drive SATA connectors. There are some computers (not many) that used non-standard connectors and required adapters. If you think that is your situation, look up pictures of SATA HDD's to see what a standard SATA drive's connectors look like. But, unless you have one with an adapter that must be removed, the connectors on your SATA HDD ought to match exactly with those in your external case.
However, there is one thing that could go wrong. If you have a case designed for an IDE drive, and a SATA drive to install, it won't work. You should only mount a SATA HDD in an external case designed for SATA drives.