OK - I will comment via my answer ...
As mentioned in another response, prior to this exchange here in Judges, the angel of the Lord has been interacting with Gods people right from the times of Moses. And, we can use these previous encounters to help answer your query “Is the Lord and the angel of the Lord the same here”.
EXODUS 23:20 Behold, I send an Angel before you to keep you in the way and to bring you into the place which I have prepared.
How many ‘entities’ are present here? It clearly differentiates between 2 entities. And, we know this is the same angel that we are seeing in Judges because in that passage in Judges 2 we see ...
JUDGES 2:1 Then the Angel of the Lord came up from Gilgal to Bochim, and said: “I led you up from Egypt and brought you to the land of which I swore to your fathers;
So here we see it was the angel that lead them - BUT - in Judges 6 we see this ..
JUDGES 6:8 [snip] “Thus says the Lord God of Israel: ‘I brought you up from Egypt and brought you out of the house of bondage;
Here it is the Lord that lead them? Where as earlier it was the angel? Are they the same? And, if so, who are the two entities in Exodus 23?
And look a little further down in Judges 6 ... v21 “And the Angel of the Lord departed out of his sight.” BUT then within the same moment, in v23 “Then the Lord said to him, “Peace be with you;”.
So here we see the angel depart, but the Lord ‘apparently’ is still there?
If you try to reason all of this out, it starts to get conflicting. But, in Hebrew ‘thinking’, it is not. The way early Hebrews both viewed and wrote about ‘representation’ has a valid explanation for this. Let start here - ..
JOHN 1:18 No one has seen God at any time.
This is supported in 1 John 4:12. So God can’t be ‘seen’. But we know He can be ‘seen’ in a representative. John 14:9 includes ‘He who has seen Me has seen the Father;’. So Jesus ‘represents’ God" when we ‘see’ Jesus, we ‘see’ God. Of course' this is easily explained by most via the doctrine of the ‘trinity’.
But, in the Old Testament, this ‘representative’ we meet in Judges(and elsewhere) is called an ‘angel’. Yes there is a supported teaching of ‘Christophonies’ which satisfies many, and I [personally] have no issues with this, but let’s look a little further..
In many ‘angel of Lord’ passages we distinctly see more than one entity, example Exodus 23. Now, because God can’t ‘be seen’, let’s stay with this, so therefore it must be a representative. And, whoever this/these representatives are, they represent God, as if they are ‘one’ with God. So if there are two entities in Judges, or elsewhere, and that is IF?, it doesn’t or wouldn’t change, or alter anything - as they are [seen as] ‘one’.
So the answer to your query is, there is One - they are the same, even if there are two separate ‘entities’. (And the Hebrew structure in some passages where the angel is present with the Lord clearly shows they are two distinct entities), they nevertheless fully, 100% represent God.