What's the official name of a 1 to 1 line plot? I'm wondering if there is a name for one to one line graphs. Is it qq-plots? Is the qq-plots applicable on all types of variables or only quantiles? In other words, what's the name of the graph that compare two variables to assess if one variable is overestimating the other in relation to a 1:1 line?
If I want to built a one to one line plot, how should I standardized my variables so that the are comparable on the one to one line? 
For example, here is a one to one line graph. 
plot(x= 1:100, y = c(12*(1:100)^(1/2) + rnorm(1,1,1)), 
     asp = 1, xlim = c(0,100),ylim = c(0,100)) ; abline(a=0, b = 1, col = "red")


In that case, we could say that the y variable is alway overestimated in comparison of the x variable. 
 A: The official name of the line is 'identity line' or 'line of equality'. And if you are comparing measured data with predicted data, or two different models, you should standardize the axis. The starting and ending point of both axes should be the same. You can also plot the trend line in the scatter plot (measured ~ predicted) to better visualize the difference between the 1:1 line and the actual trend in the model.
Mathematically, it can be written as the line where:
$$y = x$$
A: Based on your comment, I think what you are ultimately after is to assess agreement (see Wikipedia, or John Uebersax's website).  I don't think there is a name for the plot you have in mind.  I would just call it a scatterplot with a 1:1 reference line plotted.  I think that's probably fine to do.  I would not standardize your variables first, as that would prevent the plot from showing what you want to discover.  If you wanted a quantitative value to describe the level of agreement, you could compute Lin's concordance coefficient to pair with your plot.  
However, note that it is typically more difficult for people to assess agreement in this way.  You might prefer to create a Bland-Altman plot (also called Tukey's mean-difference plot).  You can see if the differences diverge from mean $0$ (and test them with a $t$-test), if the differences vary more at higher levels, if there is any residual curvature, etc.  
If you just want to see if the distributional shapes differ, you can do a qq-plot as well, but I don't think that's what you're after.  
