I believe it is about perspective. Note that "covalent molecule with ionic character" and "ionic compound with covalent character" are different.
If we are looking at a covalent molecule and assessing its ionic character, we cannot talk about polarising power, because in a covalent molecule, there would be no cation and anion to polarise in the first place. Thus, we would go by the rule: the bigger the electronegativity difference, the higher the ionic character and therefore, the more polarised the bond.
If we are looking at a ionic compound and assessing its covalent character, then we will go by the rule: the more polarising the central atom, the higher the covalent character.
Now, from the way you phrased your question, I believe that you are conflating the concepts "big electronegativity difference" and "polarising power". They are distinct concepts and should be thought of separately.
Although bond polarity is associated with electronegativity difference, "polarising power" is about the polarisation of the electron cloud of the anion by the cation and not the polarisation of the bond. This is also why "polarising power" is a concept associated with ionic compounds with covalent character.
Hope this clarifies your doubt! If you are still unclear and require some examples for clearer understanding, please leave a comment on my post.