Thanks for the all the info... Have further check with AD and found some differences.
The different has been highlighted
Case - 1950 is cushion casing while luminor is not..(as highlight by chrisyen)
Movement - 1950 is in house movement while luminor is modify movement based in eta(still not sure about this facts, hope any sifu can confirm)
Crown guard - 1950 shown reg at crown guard while luminor has no wording
Date - 1950 date window is a square one while luminor date window is have magnifying glass.
I think there is a need to clarify the situation.
Luminor refers to the basic design where the dial does not have the seconds sub dial or what is referred as base. In your question, what is the difference between the 1950 Luminor and Luminor. I am guessing the Luminor you refer are models like the Pam112? The basic difference then is the case used. The Luminor 1950 uses the 1950 case, while the Luminor uses the Bettarini case. Yes the 1950 case has more a cushion shape compared to the Bettarini case.
With regards to the above, the pam243 has a 1950 case, eta movement and magnifying glass.