motor vs servo

if i have a motor programmed to move when i hit a button, will a servo move if it is wired the same.

Quick answer: no.

When you set a servo output value, the servo will turn to a specific position and stay there.

When you set a speed controller output value, the motor will begin spinning at a specific speed. That’s an extreme simplification, but it’s close enough.

that is weird, a servo moved for us when we programmed a motor for the same pwm.

It should move, then stop at a position relative to the input (joystick position, hardcoded constant) you are giving it.
If it’s connected to a joystick it will follow the position of where the joystick is held.

It won’t stop if it’s a continuous rotation servo, instead, it will act like a motor.

Yea, then it is just a motor and not a servo except in form factor.
The ones in the Kit are traditional servos, and that’s what I assume.