The terminology is vague at best. There are no hard and fast rules, and nobody playing police when people don't use the term correctly.
Usually, but not always, a transceiver is a simple buffer that has different signal standards on the inputs and outputs. For example, an RS-232 transceiver usually interfaces TTL signals to RS-232 signals. Also, transceivers are similar to "drivers" and "receivers" except that a transceiver usually does both driver and receiver functions in the same chip.
A Phy is similar to a transceiver in that there is usually different signal standards on "both sides of the chip". With Ethernet it is MII/GMII/etc on one side and, well, Ethernet on the other. There are other Phy's that talk USB, PCIe, and many others. Phys usually incorporate some sort of SERDES (SERializer-DESerializer) function and line encoding. More sophisticated PHYs contain a mini-DSP in them to do all sorts of crazy communication things like advanced baseband wander correction.
A transceiver does not have to be associated with a serial data-- they can be used for parallel data as well. A PHY usually involves some sort of serial data stream. But this is more of a convention than a rule, and I am sure there are chips out there that are exceptions to this.