Toggle on off with two transistors
This simple circuit is supposed to toggle on and off a led light with a single button. At the start condition the led light is off; at the node 2 of the circuit the signal is high.
When you press the switch button the node 1 takes the high signal from the node 2, so both transistors switch on. Once the capacitor discharges through the collector of the Q2 transistor the node 2 takes the low signal. When you press the button again both transistors switch off due to the low signal from the node 2. This circuit works properly if the button is pressed for two seconds or less.
Toggle on off with relay
This circuit works by coil hysteresis and is supplied with 12 Volt. When the momentary button is pressed both transistors are on, but the relay coil keeps off because it is supplied with 2,5 Volt. When the button is released the relay switches on because the transistor Q2 is supplied for a bit by the capacitor. When you press the button again the transistor Q1 switches on, leads the Q2 base to the low level and discharges the capacitor. Even if the coil takes 2,5 Volt, the relay keeps on due to the hysteresis. When the button is released,the transistor Q2 would take about 10 milliseconds to switch on. But the response time of the relay is shorter, so the circuit backs to the start condition.