special relativity - Direct Product vs Tensor Product

I am confused in the notation on page 67 and page 70 a text (http://www-pnp.physics.ox.ac.uk/~tseng/teaching/b2/b2-lectures-2018.pdf), whether it's talking about a direct product or an outer product:

1. 
   
   

   On page 67, it mentioned that

   
   

   
   

   "you can take a direct product of two $j = 1/2$ representations"

   
   

   
   

   and build representations of higher j.

   
   


2. 
   

   On page 70, it mentioned

   
   

   
   

   "we can think of [the Lorentz Group] as the direct product $SU(2) \times SU(2)$."

   
   
   

   
   

In each of the above, does the author mean Direct Product or Tensor Product?