The difference between Customarily and Ordinarily

When used as adverbs, customarily means in the customary manner, whereas ordinarily means in accordance with normal custom or routine.

check bellow for the other definitions of Customarily and Ordinarily

Customarily as an adverb (manner):

In the customary manner; as is custom
Customarily as an adverb (frequency):

Under normal circumstances, normally.

Ordinarily as an adverb (obsolete):

In accordance with normal custom or routine; as a matter of established occurrence.
Ordinarily as an adverb:

Usually or as a general rule; commonly.

Examples:

"'Ordinarily I go to the match on a Saturday."
Ordinarily as an adverb:

In the usual manner; unexceptionally.

Examples:

"The man was ordinarily dressed."