The short answer to the question is "Yes" they are identical - Jesus said this seven times as recorded in the Gospel of John as listed below (my translation each time):
- John 4:26 – “Then Jesus said, ‘I am.’” [To the Samaritan woman at the well. There is a reasonable case for this being identification; However, the fact that according to John 4:28-30, the woman took this to be a statement of Jesus claim to be the Messiah, and the people believed, suggests she clearly understood Jesus import.]
- John 6:20 – “But then [Jesus] said to them, ‘I am. Fear not.’” [To the frightened disciples in the boat.]
- John 8:24 – “If you do not trust/believe that I am, you will die in your sins.”
- John 8:28 – “When you will lift up the Son of Man, then you will trust/know that I am.”
- John 8:58 – “Truly, truly, I say to you; before Abraham existed, I am.” [The Jews then tried to stone Him for blasphemy.] Note that this and the previous two mean that Jesus, in the space of this chapter of John 8 uses the unpredicated “I am” idea in the present (v24), future (v28) and past sense (v58). V24 & 28 appears to be tied to believers’ salvation as well.
- John 13:19 – “From now [on] I tell you before the occurrence, that you may believe when it occurs that, I am.”
- John 18: 5, 6, 8 – “He said to them, ‘I am.’ …Therefore, when He told them, ‘I am’, they fell backward to the ground.” [This occurred when the Jews tried to arrest Jesus in the garden. It could be reasonably argued that this is a case of identification. However, the fact that the arresting mob fell backward suggests that much more is intended here.]
In the NT unpredicated uses of ἐγὼ εἰμί (ego eimi) are only ever placed in the mouth of Jesus (Just 14 times - the other in the other Gospels) and all are used as an identifier of Jesus' divinity.
In the specific case of John 8, we have three significant cases where the tortured Greek Grammar (to fit the "I am" in) is used in three different tenses as listed above:
- John 8:24 – Present tense
- John 8:28 – Future tense
- John 8:58 - Past tense
Therefore, in line with Ex 3:13-16, John is effectively saying that Jesus was, is, and always will be the Great I AM!
APPENDIX - I am in other cases
“I am” in the Greek (NT) is, “ego eimi”. The verb, “eimi” occurs 2462 times in the New Testament in various forms, but in only about 67 of these cases is the first-person nominative pronoun, “ego” used with it. Generally, the complete form, “ego eimi” only occurs when some emphasis is required.
This present continuous verb, “to be”, is the most common in almost all languages and has several syntactical functions in Greek (eg, see John 1:1 ):
- Existence, “I am.”, ie, unpredicated
- Identification, eg, Luke 1:19, “I am Gabriel”; John 9:9, “I am [that one]”; John 10:11, “I am the good shepherd”.
- Relationship, eg, Acts 18:10, “I am with you”.
- Predication, eg, Acts 22:3, “I am Jewish”.
Thus, it is significant that unpredicated "I am" is only ever spoken by Jesus in the NT.