What does that mean that two time series are colinear? I am familiar with the concept of cointegration.
But I hear sometimes people talking about colinearity (or collinearity) for time series.
A set of points is collinear if they are on the same line. But what does that mean for time series?
Is it exactly the same as cointegration of order 1?
Or is there something stronger/different in the concept of collinearity?
 A: The wikipedia gives a good example: 

Two variables are perfectly collinear if there is an exact linear relationship between 
  the two. For example, $X_1$ and $X_2$ are perfectly collinear if there exist parameters 
  $\lambda_0$ and $\lambda_1$ such that, for all observations $i$, we have
$$X_{2i}=\lambda_0+\lambda_1X_{1i}$$

This applies directly to time series, just change $i$ to $t$. 
Two times series $X_1$ and $X_2$ are cointegrated of order 1 if they are


*

*Integrated of order 1, meaning that first differences of $X_1$ and $X_2$ are stationary processes.

*There exists parameters $\alpha_1$ and $\alpha_2$ such that linear combination
$$\alpha_1X_{1t}+\alpha_2X_{2t}$$
is a stationary process.
So the answer to your first question is no. 
The answer to your second question can be yes. The colinearity is in a sense stronger, i.e. more restricting property. From statistical point of view colinear time series are the same, i.e. if you know distributional properties of one series you immediately know the distributional properties of the other. In fact if your data have time series which are perfectly colinear it usually means that one of the series was artificialy created, for example: profit equals income minus expenses. 
A: In fact, Gujarati states: "Today, however, the term multicollinearity is used in a broader sense to include the case of perfect multicollinearity, (...), as well
as the case where the X variables are intercorrelated but not perfectly so" and proceeds to give a definition in correspondence to RockScience's definition. So, my guess would be that the two terms are related to each other by the argument given by him.
A: This is one of those areas where people use the jargon to mean quite different things and I fear there is no correct answer.  Two quite different meanings are:
a) The variables are correlated.
b) The variables are highly correlated to the point where it is impossible to estimate a good statistical model that includes these variables as independent variables (i.e., due to multicollinearity).
To work out which, if either, of these meanings is being employed you will need to ask whoever it is who used the term.
