Ethernet supports a wide variety of physical layers, using a variety of different physical mediums. Some standards never see any significant deployment at all. Some are used for early deployments of a new speed but then fall by the wayside as technology improved. Some remain in widespread use for decades.
Twinax cabling is bulky and relatively expensive but can carry high frequencies which means it can support high speeds with relatively simple modulation. Twisted pair cabling tends to have lower bandwidth.
Twinax first came onto the Ethernet scene with 1000BASE-CX. This was the first copper standard for gigabit Ethernet and was used in some early deployments but it was rapidly eclipsed by 1000BASE-T and became essentially a historical footnote.
At 10 gigabit per second things got messier. The first copper standard was 10GBASE-CX4 standardised in 2002 shortly after the initial 10 gigabit fiber standards and using four 2.5Gbps lanes on twinax cabling borrowed from infiniband. Afaict it was used in some early deployments and probablly remained "current" for longer than 1000BASE-CX did but it too has now become a historical footnote.
In 2006 the 10GBASE-T standard was developed promising 10 gigabits per second over up to 100 meters of relatively cheap twisted pair cabling. However it was plagued by power consumption issues.
Also in 2006 the SFP+ standard for modular 10 Gigabit transceivers was introduced. There had been a number of previous standards for modular 10 gigabit transceivers but all of them had been much bulkier, limiting port density.
However this created a bit of a problem, SFP+ was not suited to either 10GBASE-T or 10GBASE-CX4. SFP+ was designed around a single 10Gbps lane while 10GBASE-CX4 and 10GBASE-T were four-lane standards. 10GBASE-T was also too power hungry to accommodate in a SFP+ module, while 10GBASE-CX4 connectors were too physically big.
To mitigate this, "SFP+ direct attach" cables were created. These were designed to plug directly into the SFP+ transceiver sockets. I'm not 100% sure when SFP+ direct attach was first created, I searched the history of the Wikipedia article and that lead me to an Intel article from 2008. As I understand it short direct attach cables are passive twinax, slightly longer ones are twinax but with additional amplification and long was are fibre based. Fibre based direct attach cables can still be cheaper than separate transceivers and fiber because the transceivers only have to be good enough to work with the supplied fiber.
Improvements in signal processing technology meant that 10GBASE-T SFP+ modules did eventually show up, but they were limited to 30 meters rather than the full 100 meters and were initially very expensive. They have come down in price a bit but they are still significantly more expensive than either direct attach cables or fibre transceivers.
The idea of direct attach cables has been carried over to faster variants of the SFP standards and you can now get such cables for speeds as high as 800 gigabit per second.
The downside of direct attach cables is that they must run directly from device to device, they cannot be routed via patch panels. This is not a problem if the devices are in the same rack and may be tolerable for "next rack over" but rapidly becomes a PITA if longer distances are needed.
Twisted pair on the other hand seems to have petered out. The IEEE approved standards for 25GBASE-T and 40GBASE-T in 2016 but nearly 7 years later I still can't find anywhere actually selling them.
how does it differ from straight through and cross over cables for the connection of unlike and like devices?
The existence of straight through cables is really an artefact of the fact that twisted-pair cables used for Ethernet evolved from phone cables.
With cable types designed specifically for high speed symmetric communication it is more common that every cable is "crossed".