This quote from section 5.6 Image externalization of the pgfplots manual probably answers your question:
The external library has been written by Christian Feuersänger
(author of pgfplots). It has been contributed to TikZ as general
purpose library, so the reference documentation along with all tweaks
can be found in [7, Section “Externalization Library”]. The command
\usepgfplotslibrary{external} is actually just a wrapper which loads
\usetikzlibrary{external} or, if this library does not yet exist
because the installed pgf has at most version 2.00, it will load a
copy which is shipped with pgfplots.
(7 is a reference to the manual for TikZ/pgf.)
So yes, given that the two are identical, having one is enough.
Small correction
Stefan Pinnow mentions in a comment that because pgfplots has a faster release cycle than TikZ, the version of the library that ships with pgfplots (as per the quote above) is in fact newer, with more bugs fixed, than that in TikZ.
For this reason it would be best to use
\usepgfplotslibrary{external}
or
\usetikzlibrary{pgfplots.external}
externallibrary shipped with PGFPlots is "much newer" and has some bugs fixed. So I recommend using\usepgfplotslibrary{external}or\usetikzlibrary{pgfplots.external}which both load theexternallibrary of PGFPlots. – Stefan Pinnow Nov 30 '16 at 20:44