In this question, under Mawia's answer, Narnian made the comment:
This uses an example taken from before payment for sins were made. Thus, it does not refer to heaven, but to Paradise
What is the difference between "heaven" and "paradise"?
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In the LXX, the Greek word παράδεισος (paradeisos) was used to translate the Hebrew phrase גַּן עֵדֶן (gan eden), otherwise known in English as "the Garden of Eden" (cp. LXX Gen. 3:24).
Παράδεισος occurs in the LXX in:
Gen. 2:8-10, 2:15-16, 3:1-3, 3:8, 3:10, 3:23-24, 13:10; Num. 24:6; 2 Chr. 33:20; Eccl. 2:5; Song 4:13; Sir. 24:30, 40:17, 40:27; Psa. Sol. 14:3; Joel 2:3; Isa. 1:30, 51:3; Jer. 36:5; Eze. 28:13, 31:8-9; Sus. 1:4, 1:7, 1:15, 1:17-18; 1:20, 1:25-26; 1:36, 1:38, 1:54
Παράδεισος occurs in the ΝΤ in:
Yeshu'a told the thief on the cross, «σήμερον μετ᾽ ἐμοῦ ἔσῃ ἐν τῷ παραδείσῳ», that is, "Today you shall be with me in the Paradise."
In his second epistle to the Corinthians, the apostle Paulos wrote how "a man in Christ...was caught up unto the third heaven." He then elaborates that this man was likewise "caught up into the Paradise" (ἡρπάγη εἰς τὸν παράδεισον).
Some interpret this as meaning that this man was caught up unto the third heaven and then into Paradise. If this is so, should we understand it that the Paradise is even higher and loftier than the third heaven?
I believe the Orthodox church thinks they are all the same place:
A great reward is prepared for the righteous in the future life (Matt. 5. 12). They will be brought to the most perfect and beautiful place, which the Holy Scripture calls Paradise (Luke 23. 43), Heaven (Matt. 6.9), the Kingdom of God (Luke 13. 28-29), the heavenly Father's house (John 14. 2), the city of the living God and the heavenly Jerusalem (Heb. 12. 22-23).
I think Paul's mention of the 'third heaven' is more likely referring to something different entirely: Beri'ah, the third of four celestial 'worlds' in Judaism which would indeed be less glorious than Paradise.