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.

In Deuteronomy 28:22, this signifies a disease or sin that afflicts the spirit. (Arcana Coelestia 8364[3])

In Leviticus 13:28, this signifies what is externally clean or whole. (Arcana Coelestia 10206)

In Isaiah 5:11, this signifies the fire of the love of self and the world. (Apocalypse Explained 405[45])