The IEEE 802.3 standards define certain L1 characteristics/operation, but do not define the connectors to use to connect the devices.
For instance, while 802.3 does define that 100BASE-TX will use twisted pair cabling that must meet certain characteristices (attenuation, cross talk, etc), it does not define if this must be UTP or some variation of STP. It also doesn't define a certain "Category" of cabling, although typically the cabling "Categories" are designed to meet specific requirements of the 802.3 standards.
With reference to the standard not defining the connector, this is probably best illustrated using fiber as an example. The 802.3 standards define the characteristics/operation of 1000BASE-SX, but you can find 1000BASE-SX connections that use LC, SC, MTRJ, ST or a number of other types of connectors. As long as the connector allows the connection to meet the requirements of the standard, it is perfectly okay to use it.
As to why the cables are called Ethernet cables, I have already addressed that in this answer to a previous questionthis answer to a previous question, so it is probably better to view that answer as well rather than for me to copy it here.