Basically, when a company refinances, the bonds will be trading at a premium, as market yields will be lower, coupons for new primary issues will be lower, and the company can issue lower debt. Existing holders of callable bonds will be disadvantaged as bonds will probably be called and refinanced, this will disadvantage investors.
An entity who took out a mortgage can prepay the mortgage (refinance with another mortgage). The investor or entity at the other end of the mortgage will be disadvantaged.
Both present a similar risk of repayment, although prepayment risk can be more of a gradual thing than call risk. Both have increased reinvestment risk.