examination vs self-examination

examination and self-examination both are nouns.

Word	Noun	Adjective	Verb	Adverb
examination	Yes	No	No	No
self-examination	Yes	No	No	No

As nouns, self-examination is a hypernym of examination; that is, self-examination is a word with a broader meaning than examination:

examination: a detailed inspection of your conscience (as done daily by Jesuits)
self-examination: the contemplation of your own thoughts and desires and conduct

Other hypernyms of examination include introspection, self-contemplation.

examination (noun)	self-examination (noun)
the act of examining something closely (as for mistakes)	the contemplation of your own thoughts and desires and conduct
the act of giving students or candidates a test (as by questions) to determine what they know or have learned
a detailed inspection of your conscience (as done daily by Jesuits)
a set of questions or exercises evaluating skill or knowledge
formal systematic questioning