While these terms are still used sometimes, the actual interfaces are long obsolete. AUI is the 10 Mbit/s interface between the MAC (within the NIC) and the external transceiver PHY for e.g. 10BASE5 or 10BASE-T).
A MAU is an external transceiver connecting to the AUI, e.g. the extremely obsolete vampire tap for 10BASE5 or a pocket transceiver for 10BASE-T. This is the exact precursor of more current GBIC, SFP, XFP, SFP+, CFP, ... pluggable modules.
The successors of AUI still exist as MII (Fast Ethernet), GMII (gigabit), XGMII, XAUI (10G), ... and their variants. As with AUI, these interfaces are optional and may not physically exist in a given device.
Sometimes "AUI" is still used when people refer to a visible transceiver interface like you very commonly see inside an SFP slot. (edit: removed the references for S/GMII and XGMII since SFP/+ use a lower level interface.)