Is time exchanging the same as bartering?

No. Bartering is based on the cash economy in a one-to-one relationship.  For example, a plumber and carpenter agree to each provide $1000 worth of work on each other’s homes — that’s the cash world. In the exchange economy, the services are based on time, not cash. Each service hour is valued the same, and they are exchanged within a network, not one-to-one.