I am not sure whether this is really a standard terminology, but here goes.

I believe that inward and outward are references to the diffusion of Ni in intermetallic layers grown by aluminizing Ni-base superalloys (used in gas turbine engines).  This is a function of the aluminum activity, temperature and time when pack aluminizing the Ni-based part in a mixture of Al(pure or alloyed), alumina and a halide at a temperature in the range 750-1100^oC.  
The intermetallics NiAl₃, Ni₂Al₃, NiAl and Ni₃Al are present in the Al-Ni phase diagram (http://klara.met.kth.se/pd/element/Al-Ni.html).  

The morphology of the aluminized Ni-base alloy can be controlled by the Al activity of the pack.  “A high activity pack causes Ni₂Al₃ to be the predominant phase with the diffusion of Al inward [my emphasis] being greater.  Most processes aim at the beta NiAl phase which is more suitable and resistant with favourable mechanical and oxidation properties.
…
“Aluminum can move at a relatively high rate through Ni₂Al₃ in the inward diffusion type of coating while in NiAl only Ni can diffuse significantly and does so at a relatively low rate.”
Thus, a low Al activity pack allows a greater proportion of the more desirable NiAl phase (which grows by outward diffusion of Ni) in the coating formed.  Alloying additives such as Cr form Cr-rich interlayers which act as barriers against Al diffusion.  These alloying elements also affect the morphologies of the phases; columnar morphology is bad.
---Metallic and ceramic Coatings, M. G. Hocking, V. Vasantasree and P. S. Sidky, chapter 5 (1989).

An online description of the above: Coatings for High-Temperature Structural Materials: Trends and Opportunities (1996), pp. 78-82, ‘Manufacturing Technologies of Coating Processes.’
http://books.nap.edu/books/0309053811/html/78.html#page...

I've only found one reference to inward and inward coatingd and that was in an older American Society for Metals manual. They said as above that for inward Al. is the net diffusing specie, applied to nicket based superalloys. Outward diffusion coatings are applied to cobalt based superalloys. It does not be a common term. ASM also has books on Thermal Barrier Coating (TBC).