Nope, that not correct. Before going to the correct definition of volumes and open interest, let us understand that both these terms viz. 'Volume' and 'Open interest' are applicable to both futures as well as options.
Volume = No. of shares transacted over a period(ex: day).
If trader A sells 1 share to trader B, the volume is recorded as 1. If Trader B sells his 1 share to trader C, then the volume count increments to 2.
Open interest = No. of outstanding contracts for a particular contract(Future/option, strike price, expiry, underlying)
If trader A sell an option contract to trader B, then volume is recorded as 1(explained above) and Open Interest increases to 1. If trader B sells his option to trader C, the volume increments to 2 but Open Interest remains at 1.
Open interest changes only when positions are added/closed, irrespective of the no. of trades.
However, volume increases irrespective of change of open interest as and when the contract is traded.
I hope you got the point.