I believe that the answer has been provided, mostly in the comments but here is a short summary:
The mathtools package loads the amsmath package, if it has not already been loaded. This is common in many packages that need to ensure that dependencies are loaded. If you have a look in mathtools.sty line 60, you will see:
\RequirePackage{amsmath}[2000/07/18]
As such if you only load mathtools, you will have both packages loaded and you do not need to \usepackage{amsmath} in your preamble. To see this you can run the following minimal:
\documentclass{article}
\usepackage{mathtools}
\makeatletter
\@ifpackageloaded{amsmath}{
\AtBeginDocument{True amsmath is loaded\par}}{}
\makeatother
\begin{document}
\end{document}
Certainly mathtools is not a replacement package for amsmath. This is clear from the package author's comments in the abstract and the introduction:
The mathtools package is an extension package to amsmath
Hope the above will help you a bit more as to how to find your way around LaTeX and the many packages that are available.
mathtoolsis an add on toamsmath– Marco Daniel Feb 08 '12 at 18:42mathtoolspackage includes theamsmathpackage. – Peter Grill Feb 08 '12 at 20:50loadmight be a better word,mathtoolsdoes not come with its own version ofamsmath;-) – daleif Feb 09 '12 at 09:00mathtoolsis\RequirePackage{amsmath}, so that contents ofamsmathare included/loaded/imported bymathtools. Since I do not know ofloadas being part of the LaTeX syntax, I think include would be a better choice (but did not use syntax highlighting as inincludeto indicate that it was a keyword). English not be my bestest :-) so leave it up to others to select the correct word. – Peter Grill Feb 09 '12 at 15:35