Algorithm Analysis: In practice, do coefficients of higher order terms matter?

Consider an^2 + bn + c. I understand that for large n, bn and c become insignificant.

I also understand that for large n, the differences between 2n^2 and n^2 are pretty insignificant compared to the differences between, say n^2 and n*log(n).

However, there is still an order of 2 difference between 2n^2 and n^2. Does this matter in practice? Or do people just think about algorithms without coefficients? Why?