Accelerator rider
An accelerator rider accelerates the death benefit of the insurance plan. This is how the plan works. For instance:
Tom (so sorry to use your name if you are also Tom

) buys a Life insurance of that covers death 300k, TPD 300k and CI 300k (accelerator). 5 years later, he falls suffers an heart attack that requires surgery and it is claimable under his CI rider benefit. The full 300k is paid out and the whole plan terminates.
Hence, once the plan terminates, the death benefit stops as well. So if two year later Tom pass away, his family would not get any insurance payout under this plan that Tom has.
Waiver Rider
I usually see this rider added into a term plan. On the onset of a critical illness or undergo surgery as covered by the plan, the premiums of the plan and any other attaching rider is waived off.. This means that you won't have to pay any premiums when you activate the benefit of this rider. No money is paid out. Waiver riders are usually till age 65
Additional rider
This rider provides additional coverage that is added on to the basic plan.
Using Tom for our illustration again:
Tom buys a Life insurance of that covers death 300k, TPD 300k and CI 300k (additional). 5 years later, he suffers an heart attack that requires surgery and it is claimable under his CI rider benefit. The full 300k is paid out and the plan continues. IF 2 years later, Tom pass away, his family will then get the 300k death benefit as well.
To understand the difference of accelerator Vs Additional in another manner,
The basic plan that covers death is like a basketball hoop. When the ball goes through the hoop, the benefit is paid out.
Hence, an accelerator works by increasing the size of this hoop to make it bigger and easier for the ball to go through.
But for the additional rider is that it like another hoop that is placed beside the main hoop.