Right definition of linear grammar
They second quote from Wikipedia has lost its context. Here it is complete, with emphasis added:

Another special type of linear grammar is the following:

linear grammars in which all nonterminals in right hand sides are at the left or right ends, but not necessarily all at the same end.


A linear grammar has at most one non-terminal on the right-hand side of any rule, as per Linz' definition.
But any linear grammar can be transformed into an equivalent linear grammar of that special type, simply by adding a new non-terminal. Wikipedia goes on to show an example of this transformation. So it is possible to assume wolog that a linear grammar is in that form, if it turns out to be helpful.