Difference between no perfect multicollinearity and no multicollinearity Some textbooks (for example, Introductory Econometrics: A Modern Approach by Jeffrey Wooldridge) assume that no perfect multicollinearity for the OLS regression, while others (for example, Econometrics by Fumio Hayashi)  just assume that no multicollinearity. Are there any differences between these two assumptions? and what are the differences?

Thanks in advanced!
Perfect multicolinearity means that two independent variables are perfectly correlated with their $r^2=1$ multicolinearity technically refers to any non zero correlation between two independent variables but when it is mentioned as a problem it usually implies that the correlation is high. So there is a difference between the two terms perfect multicollinearity is a special case of multicolinearity. 

Also they have different implications for OLS. Under perfect multicolinearity OLS cannot be identified. Under high muliticolinearity OLS can be identified but standard errors will be inflated.

However, to make the things confusing, I noticed that sometimes people use the terms interchangeably. I only have the Wooldridge book so I can’t check the text of the other one to compare it but I think they actually refer to the same thing.