Callable Bonds - A bond is callable if the issuing company can redeem the shares before the maturity date. For example, you bought a 10 year bond from XYZ company. XYZ can call the bond after 5 years at 101. This means after 5 years, XYZ can force you to give up your bond, but they’ll pay you 101% of par value. What are the disadvantages to the purhcaser? He/she has to give up the bond and will not be able to collect the coupons anymore. The principal is returned which exposes this bondholder to reinvestment risk. Why would a company want to do this? If market interest rates have decreased to the point where XYZ can issue new bonds that pay a lower coupon, it will be worth it for XYZ to call the existing, higher coupon-bearing bonds to issue new, lower coupon bonds. The interest payments will then be lower for XYZ.
Refundable Bonds - If a bond is refundable, XYZ can call your bonds and pay them off using the proceeds from a lower-coupon issue (the situation described above). If a bond is non-refundable, then XYZ can’t use the proceeds from a lower-coupon issue to do this. But, a bond can be both callable and non-refundable. In this case, XYZ would call your bonds, but they can’t pay off the principal with the proceeds from another lower-coupon issue. They can, for example, pay it off instead with straight cash from a general account.
I’m not sure if this is plain English. And yes, whoever is randomly chosen to be paid off sooner through a sinking fund provision is at a disadvantage assuming they wanted to hold onto the bonds. It’s similar to your bond being called. You are forced to redeem your bond.