Is principal component regression (PCR) using principal component scores for regression? Principal component regression (PCR) in fact is regression on PC scores but not PCs. Why then in so many books and tutorials do they say something like, 

in statistics, principal component regression (PCR) is a regression analysis that uses principal component analysis when estimating regression coefficients

(wiki), and also in the famous book Principal Component Analysis (Jolliffe, 2002, page 169) it says

... which [PCR] has simply replaced the predictor variables by their PCs in the regression model

It makes me quite confused.
 A: I think the wikipedia article is being a little sloppy in saying "uses principal component analysis when estimating regression coefficients".  Better might be something like "uses principal component analysis to create explanatory variables before estimating regression coefficients."  There's nothing objectionable in the subsequent sentence "In PCR instead of regressing the dependent variable on the independent variables directly, the principal components of the independent variables are used."
I also don't see anything wrong with your quote from Jolliffe's book (which I haven't read).  It is correct that PCR uses principal components of variables as the predictor variables in a regression model.
I don't quite understand what you mean by "regression on PC scores but not PC".   You first conduct principal component analysis to create the scores and then use those scores in the regression.  
A: The other answers use a different terminology than what the author may be familiar with. Below, I refer to the scores matrix and use principal components to refer to the unit variance eigenvectors.
If you consider the answer as applied to the general case of in-sample and out-of-sample regression, then knowing the principal components matrix is sufficient to perform PCR, but knowing the scores matrix is not.
Principal component analysis
Given $X$, an $m \times n$ matrix, in PCA we find $T$, $P$ such that $T = PX$ where $t_1,\dots ,t_n$ are uncorrelated and arranged in order of decreasing variance. $T$ is called the “scores” and $P$ is called the “principal components.”
Principal component regression
To regress design matrix $X$ onto response vector $y$ using PCR, first find the principal components of $X$ using PCA. Then, using the first $k$ principal components from $X$, perform ordinary least squares of $P_{k}$ onto $y$.
Algorithm overview
Using ordinary least squares, solve $Y=PXB$, where $B$ is the matrix of coefficients. So in the sense that in regression we do operations on $X$, you just need the principal components (i.e. eigenvectors) and design matrix ($X$) but obviously $PX=T$ is the score matrix.
Now suppose you evaluate your $B$ on new data $X'$. You still need the principal component matrix $P$ (up to $k$ components), but do not need $T$. Thus, PCR uses the PC matrix but not the scores matrix in the general case.
Answer sourced from A Simple Explanation of Partial Least Squares, by Kee Siong Ng (2013).
Thanks to @amoeba for help clarifying this answer.
