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i am not sure a single clock source will generate 2 clocks with same frequency with unknown phase relationship.
even such source is there use only one clock from that source for both the blocks that are exchanging data, instead of synchronizing the data paths between the blocks.
In general for...
I did not clerly understand following statements
"two clocks name Clk1 and Clk2 from the same clock source and the frequencies of both the clocks being same"
"the clock is send to different designs"
i think, No need of a synchronization circuit between the paths of two designs.
your first statement is correct, with postive skew, there is more time to the signal to reach the destination for setup slack analysis so the time period decreases.
but it may violate hold slack
and the skew effect very little on frequency of operation.