Currently the Drupal core codebase is scattered with references to both "install profiles" in some places and "installation profiles" in others.
We should standardize on one single terminology, above all, for consistency in documentation.
"Installation profile" is more natural sounding language. I decided to consult what the codebase uses so see if that would sway the vote, but sadly, there is no measurable consensus or consistency there either:
* 34 instances of "install profile"
* 38 instances of "installation profile"
Most, if not all, of the references to "install profile" are in code comments, while "installation profile" is used in user-facing strings, but there are exceptions. core/includes/install.inc uses "install profile" consistently while core/includes/install.core.inc uses "installation profiles". CHANGELOG.txt uses "install profile". The two core installation profiles both use "install profile".
A Google search for "drupal install profile" turns up the top 6 results having "installation profile" in their title.
A search for both "install profile" and "installation profile" on the Drupal core issue queue shows that most issues have "install profile" in their titles, presumably for brevity.
On #1539940: Encourage best practices in /sites/README.txt, /modules/README.txt, /profiles/README.txt and /themes/README.txt, we decided to go with "installation profile", for readability. This is a follow up issue to bring the rest of the codebase into consistency.