Western bridle type for a draft horse that also drives

The previous owner of my recently purchased Belgian mare told me he used a snaffle bit on her. He also said she does not neck rein, only direct reins because she is trained to drive and ride. As I looked for a draft bridle and bit for her, I saw a side pull bridle. What exactly is this, and is this the kind of bridle I should get for her, instead of just a regular Western bridle with snaffle bit?
Thanks.
Maureen