Hello,
I am starting a new project where I am planning on creating a "ball and table" style project. I have been doing research online but I am very confused as to if I only need an accelerometer to determine if the table is level or an IMU (accelerometer and gyroscope combination). Many other forums I have found people simply just define what the devices measure, but I am asking would using an acceleromotor alone provide high enough accuracy for the small adjustments required to keep the ball from rolling over the edge or would I need to use an IMU to achieve the desired accuracy and response time?
thanks 
When something is in motion and you need the pitch, roll and yaw, then you need the sensor fusion and a filter, for example a AHRS filter.
If you want to measure the angle for a electronic spirit level, then you need only the accelerometer.
I think that commercial electronic spirit levels use only a accelerometer.
Your table is in between those things.
A accelerometer is just as accurate as the sensor fusion. However, a accelerometer is sensitive for vibration. If the motors cause too much vibration, then you need a software filter for the accelerometer and that makes it slower. In that case the sensor fusion with AHRS filter might be needed.
It is a good question and I can not guarantee that only a accelerometer will work. To me it feels that you are going to need the sensor fusion in the end for smooth and fast operation.
I suggest to buy a sensor that has at least both an accelerometer and a gyro, for example a MPU-9250, LSM9DS1 or perhaps the BNO055.
Some old outdated "IMU" boards use a number of different sensors or have an analog output. Modern sensors have everything in the same chip. The "Kalman" filter is also outdated.
Start with the accelerometer data and see how far you get.
Tilt sensing is done by the accelerometer, which detects the acceleration due to gravity and the angle that the "down" direction makes with the accelerometer axes.
This is inaccurate if the object to which the accelerometer is attached is accelerating or rotating, so the gyro helps to compensate for the errors.
I agree with Koepel to start with just the accelerometer and see if that works well enough. A good intro to tilt sensing is found on this page, with correct roll/pitch example code. See the "sample sketch". (Note that there are plenty of sites posting incorrect accelerometer tilt code)
@Koepel (sorry I'm new to this and don't know if this is the proper way of "tagging" people). Thanks for the reply. That is just the advice and information I needed.