I understand basis points to be absolute difference in some rate, where the rate was expressed as a percentage. So, if the interest rate was raised from 5% to 5.25%, we don't say the increase was 0.25% (because that could be interpreted as understating the change) and we don't say the increase was 20% (0.25% / 5%) because likewise that would overstate the change. We say the increase was 25 basis points to avoid any confusion.
I understand basis points to be absolute difference in some rate, where the rate was expressed as a percentage. So, if the interest rate was raised from 5% to 5.25%, we don't say the increase was 0.25% (because that could be interpreted as understating the change) and we don't say the increase was 20% (0.25% / 5%) because likewise that would overstate the change. We say the increase was 25 basis points to avoid any confusion.