There were several versions of BIOS (Basic Input Output Systems) that came on motherboards in the 1990s and 2000s that had an option to choose when to resume. These systems usually had an entry named "Resume From S3", and allowed you to select from several options, such as "any key," "power key," or "wake key." However, in all cases, there were other optional means of resuming, usually by hitting the power button or even a sleep/wake button built into the case that was directly wired to the motherboard. The wake button is largely obsolete (I don't think I've seen one in the past decade).
The S levels are defined by ACPI, where each increase in S level results in further power savings at the expense of how long it takes to resume normal operations. S0 simply turns off the monitor(s)/video cards, S1 turns of non-critical devices and suspends CPU usage, S2 flushes CPU buffers for additional power savings, S3 powers off the CPU entirely (but the RAM retains power), S4 is the so-called hibernate level (suspend to disk), and S5 is "fully shut down" (full reboot required to start up again).
Devices with S4 resume options can be resumed even while hibernate is active. Without S4 resume options, the only way to wake a system in hibernate is by pressing the power button, but other options can monitor the system inputs (e.g. USB keyboard, PS/2 keyboard) for a valid wake signal, such as the Wake key.