In the first diagram, the three lines will be address, data and control busses.
There are various schemes, but in some way a DMA controller has to intercept and be able to override the address, I/O and memory control signals, to be able to do transfers outside of the CPU programmed instructions - but still pass the control lines through for normal CPU access.
The data bus may be common and used directly, eg. by the DMA controller commanding a memory read and I/O write (or vice versa) while the CPU is not accessing the data bus, or it could work as a proxy and eg. do synchronous accesses to memory and separate async access to the I/O device, storing and transferring a word in whichever way is needed.