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What's the difference between the 40nm and 45nm technology nodes? Could they be considered as the same node?

You can say both are same or 40nm is sub-node of 45. We can shrink 45nm to 40nm to get more number of dies per wafer.

sir is it possible 40nm technology node? since i have studied in one of your post a technology node is factor square root times of previous technology and before it we have 65nm technology node

Technology node is still 45nm. But as Narveer told, this is to get more die per wafer, foundry shrink 45nm geometry to 40nm. So all 45nm GDS are shrunk to 40nm before fabrication.