In what case you would say "I speak things" instead of "I say things"?
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I speak things means something like I proclaim things, pertaining authority, like I speak things into existence. I say things is way of normal discourse.
Which is only a problem if the things I speak have certain authority or effect. Usually I would use this phrase if the things I spoke had a proclaiming character and hurt a situation or person.
In ordinary speech, "speak" does not take a direct object. You can be speaking, you can speak to somebody, but to "speak words" or "speak a message" is unusual and I would say literary. (I except idioms like "speak my mind" and "speak the truth", and also the construction "Speak English", where the language looks syntactically like a direct object, but I actually think it is a verbal modifier, like an adverb).