They are talking about different stuff. Geometric algebra is here the name used for the popularisation of a brand of Clifford algebra. The popularisation books are often written by physicists and engineers, and their maths is shaky, because they care more about applications than about proofs and rigour.
There are exceptions, for example I like the two books by Alan Macdonald about the topic:
There are exceptions, for example I like the two books by Alan Macdonald about the topic:
http://www.faculty.luther.edu/~macdonal/