What is the name of the electrical latch with one toggle input?
I think you are describing either a Latching Switch Push button compared to two momentary switches?

Or you could be describing a Toggle Flip Flop circuit connected to a momentary switch?

They look something like this, they don't need the clock signal and can just work with the feedback and Toggle inputs.
If you have a microcontroller you can write this functionality in software and make any trigger input work like this.
This is not a very well worded question, what is the context of this question?