A family of Microsoft word processing software products for creating web, email, and print documents.
Fundamental difference: Save As creates a different file, Save updates the current file. Notice that when you Save a new file for the first time you are prompted but there is no further need for a prompt unless you actually close the file.
Other than that there is no real distinction. Some of what Phillip refers to may have been fairly accurate in the days of binary file formats, but doesn't apply to contemporary OOXML files types... they are handled in a completely different manner.
On the same subject: It sounds like you may be looking for some sort of confirmation or 'reassurance' that the Save occurred. If so, note the leftmost of the 3 stoplight buttons in the upper left corner of the document window. If a dot appears within the button the document contains unsaved changes. When you save the dot goes away. This is a standard feature of OS X.
Additionally, when you Save glance at the Status Bar to see the progress indicator provided by Word.