What is the meaning of a "soft" latch?
Have a look at Soft latch power switch circuit. The article states:

Dаvid Jones through his Youtube channel EEVblog described in detail how to design a cheap soft latch power switch circuit, using one push button switch to toggle your circuit power on and off with the following design requirements:

Zero power when off.
One on/off switch.
Standalone(no MCU).
General components only (Diodes, Transistors, ..ect).
Minimal parts.


Not all those features are required to satisfy the &quot;soft-latch&quot; requirement but I think the important one is number 2 and possibly that the circuit will reset to off after a power cycle.
Examples of a hard-latch would be a standard toggle switch (as opposed to a momentary push-button style), a toggling relay (which will stay put until electrically kicked the other way) or, perhaps, an electronic controller with some kind of memory that will power up in the same state it was in before the power cycle. (This last one is trickier than it seems. There have been several questions on this site on the topic of a 1-bit memory for similar purposes.)