Angel of the LORD

In the Old Testament, somebody called 'Angel of the LORD' shows up a lot. Sometimes, this person/angel confuses the understand the characters in the story. In Genesis 22, it was 'the Angel of the LORD' who stopped Abraham from killing Isaac. Also in Exodus 3, 'the Angel of the LORD' calls Moses from the burning bush.

In either passage, the following portion suggests that the one who is present is the LORD Himself. 

As I was checking the translation of both stories, there seems to be some confusion of character. A word/sign used for 'Angel of the LORD' is something like a being which has a wing, so this being is considered a different being from the LORD Himself. But, this being talks as if he is the LORD.

The word 'Angel' has a very strong imagery, the being with wing, and in many cases that's a female like figure. It might be this 'image' the translators had when they were translating these portions.

The word 'angel' is from 'αγγελος' in Greek and in either Hebrew or Greek, they mean 'messenger.' In the OT passages above, 'Angel of the LORD' is 'מלאך יהוה’, and again, this should mean 'the messenger of the LORD.' In NT, equivalent expression would be 'αγγελος κυριου'. So, now what can be 'messenger'? Does it have to be a being? 

I have never come across in NT that 'αγγελος' denote non-being (I might be wrong, but that's my observation). 

According to the Word Biblical Commentary, in many part of Pentateuch, this expression of 'the angel of the LORD' can mean the sign/symbol/representation of the LORD. That means, this 'angel' may not mean a being apart from the LORD, rather it is part of the LORD. So, it may be like the Sun and the radiation from the Sun. The Sun is understood to be the LORD and the radiation as the messenger... 

That would solve the problem of understanding, but it would be still difficult to translate... I guess.