It just depend on the site you are seeing, on market charts/stats (like http://bitcoincharts.com/ or http://bitcointicker.co/) volume refers to trade volume, which indeed is not the money sent to the exchange, it is the BTC that changed hands inside the platform (there is no need to come from external and the same "coin" can be traded several times a day).
Sites that give information about a coin in general like http://coinmarketcap.com/ or http://blockchain.info uses Volume as the sum of the value of all transactions in the public ledger (blockchain), I am not sure if that includes mining transactions or not.
As how exchanges work, no trades in exchanges leave a trace in the blockchain, as they are just internal movements between exchange accounts, they only leave trace when people fund or withdraw coins to/from the exchanges.
Both volumes are unrelated, the first Volume (markets) gives you information about quantity of people wanting to buy or sell coins with fiat (or invest in them) while the second is real usage of the coin being handed between users, merchants, exchanges, etc.
