There are two types of buttons:
Toggle
Push the button turns it on and it stays on until you push it again to turn it off. These are often used for things like light switches.
Momentary
When you press the button the switch makes contact for as long as you hold down the button. You determine how long the "moment" will last by how long you hold down the button. Arcade button microswitches are a great example of momentary switches.
Yes and no.

Don't confuse the physical/mechanical characteristics with the behavior.
For instance, you can have a
momentary toggle.
Examples on the physical side are toggle, slide, pushbutton, foot, rocker, blade, rotary, etc...
On the behavior side, there are momentary, on-off, on-off-on, on-on and so-on

.
Of course there is also a description of the number of contacts, whether the switch is normally on or off and how it mounts.
So, if I'm not mistaken, an arcade button assembly would be considered a
Panel mounted SPDT Momentary Micro-Switch Pushbutton.
For what it's worth,
RandyT