Both Present at Once

The identification runs so close that the texts "make the Angel of Yahweh indistinguishable from Yahweh." Exodus 3 is the obvious case - the angel appears in the flame, and the speaker says I am the God of your father.
But that is only half the picture, and the other half is what makes this two powers rather than a costume. In some passages Yahweh and the Angel are "simultaneously - but separately - present."
Gideon is the clearest. The angel of the LORD sits under the oak and speaks with him. Then the LORD turns to him and speaks. Two figures, one scene. And when Gideon realises who he has been talking to he expects to die - the standard reaction to seeing God, not to meeting an angel.
Genesis does the same thing at Sodom, in one verse: the LORD rained fire from the LORD out of heaven.
Scripture links:
- Judges 6:11-24 - "the angel of the LORD... and the LORD turned to him and said."
- Exodus 3:2-6 - "the angel of the LORD appeared"... "I am the God of your father."
- Genesis 19:24 - "the LORD rained... from the LORD out of heaven."
Distinguishable, and never separate.