What is the different between an install profile and a drush make file?
Drush make...


  Drush make is an extension to drush that can create a ready-to-use drupal site, pulling sources from various locations. It does this by parsing a flat text file (similar to a drupal .info file) and downloading the sources it describes. In practical terms, this means that it is possible to distribute a complicated Drupal distribution as a single text file.


Note that it doesn't install/set up the site for you - it merely downloads and prepares the required files in the specified locations.

Install profiles...


  Installation profiles provide specific site features and functions for a specific purpose or type of site. They make it possible to quickly set up a complex, use-specific site in fewer steps than if installing and configuring elements individually.


Once you've used Drush Make to download all the files relevant to your project, you go ahead and install Drupal as normal (whether through the UI or with Drush), except you choose your profile during installation.

The code in the profile enables required modules, sets up initial configuration for those modules and the core system, perhaps installs demo content (think Commerce Kickstart), adds menus, sets variables, etc.

Using Drush make to install a profile would be a good question/answer to look at to get an idea of how they can integrate together.