[`drupal_set_message()`][1] is a Drupal core function that sets messages to be output on the next page view. `drupal_print_message()` is, I believe (based on the examples I found in Google), something people occasionally say by accident when they actually mean `drupal_set_message()`, but not a real function.
Note: there is a [`dpm()`][2] function in the [Devel][3] module, which is short for "drupal print message" that outputs variables for development debugging.
[1]:
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[2]:
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[3]:
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