It is the same thing. Let me explain.
- The "Angel of the LORD" is the LORD Himself as explained in Exodus 23:21 Angels Forgive? and reproduced in the appendix below.
This is confirmed by the fact that this "Angel of the LORD" can forgive and only God can forgive. Mark 2:7, Luke 5:21, 1 John 1:9, Amos 7:2, 5, etc.
- When Israel sinned by creating the golden calf (Ex 32:1-8), God threatened to abandon them and make a nation out of Moses (Ex 32:9, 10). Moses then interceded (Ex 32:11-13) and God relented (Ex 32:14).
However, this still left open the question of who would lead Israel and Moses wanted assurance that the Angel of the LORD (Ex 23:20, 21), namely, God Himself would continue to lead the people. This Moses specifically requests in Ex 34:9.
Thus, Moses' request to God is not out of fear but is seeking an assurance that God would continue to lead Israel despite their (forgiven) sins.
APPENDIX - Angel of the LORD
The following passages make it clear that the “Angel of the LORD” is almost always, the LORD (Jehovah) Himself, probably the pre-incarnate Jesus in particular. Gen 16:7-13, 22:11-17, 32:24-30, 48:16, Ex 3:2-6, 23:21, 22, 32:34, Num 22:22-35, Josh 5:13-15, Judg 2:1-4, 6:11-23, 13:3-23, Isa 63:9, Dan 3:25, 28, Hos 12:4, 5, Zech 3:1-7, Mal 3:1, Rev 8:3-5, 10:1-10, 18:1, 20:1-4.
A closely related phrase, “Angel of God” who is clearly God as in Gen 6:13, 8:15, 9:8, 17, 15:13, 17:3, 4, 21:12, 16-21, 35:1, 10, Ex 4:3-8, 6:2, 23:20, 21, Deut 1:6, 1 Kings 12:22, etc. See also Acts 10:3, 4, Gal 4:14.
In Isa 63:9, “the Angel of His [LORD’s] presence saved them”, and is almost certainly a reference to the same being.
The same is true of Ex 23:20, 21.
In other places we see that the LORD sends the LORD:
- Zech 2:6-12 – the LORD (= YHWH) claims three times that He has been sent by the LORD.
- Isa 48:11-16 – again, the LORD has been sent by the LORD.
Thus, unsurprisingly, Jesus is the messenger to the human race and underlines the importance that the Godhead places upon such messages.
This is not to suggest that Jesus is an angel in the sense that He is less that God; far from it! However, the Greek and Hebrew word for “angel” simply means messenger and it is in this sense that Jesus is the messenger in the above passages and under-scores the importance that God places on some of these messages that are personally delivered.