The main difference between the two switches is the mechanism they use to light the blade. Imagine one of those big throw switches in button form. That's a latching switch; you throw it to allow the electrical contacts to touch and power to flow, then throw it the other way to cut the power and turn it off. In button form, the contacts are not touching unless the button is pressed down, where it latches kinda like the end of a push pen. Then you press it again the contact pops out again and cuts power to the saber. To wire this up, it needs to be placed in series with the battery contact.
For the momentary switch, it's a bit different. They're designed to allow a signal to flow when pressed, but don't latch. If you wired it in a warrior saber, you would have a situation where you would have to hold down the button to keep it on. Luckily, these are wired up directly to the soundboard instead. Their job is to send a pulse, which the logic on the board interprets as a press or a hold. Then the board determines what to do based on its current state.
If you used a latching switch here any time the button is latched it would read as a constant pulse that the saber would interpret as a held button. For an effective 'press' you would need to quickly latch and delatch the switch.
Another thing to note is that, in a Champion or Hero tier saber, the board is always on unless the kill key is inserted. That's because the switches don't actually cut the power; when 'off' the board is actually just in a lower power mode with most of its outputs disabled. The kill key effectively separates the contacts directly to the battery, preventing the board from receiving power in the first place.