Like "say," the word "speak" refers to thoughts and feelings moving from our more internal spiritual levels to our more external ones -- and ultimately from the Lord, who is in a sense the most internal spiritual level of all. This is generally called "influx" and "perception" in the Writings, meaning they are thoughts and feelings that flow in in a complete way from the Lord, rather than being things we have to think about and figure out. On a number of occasions "speak" and "say" are used together; in these cases "speak" refers more to intellectual instruction in matters of thought and "say" refers more to feelings and affections that flow in directly.
Jeremiah 11:21-22
21
Therefore thus says Yahweh concerning the men of Anathoth, who seek your life, saying, You shall not prophesy in the name of Yahweh, that you not die by our hand;
22
therefore thus says Yahweh of Armies, Behold, I will punish them: the young men shall die by the sword; their sons and their daughters shall die by famine;