Whilst focal seizures begin in one hemisphere of the brain, generalized seizures originate in neural networks that span both hemispheres.1 Furthermore, a seizure can start focally and then spread to both sides of the brain.1

Reference:

1.Stafstrom CE, Carmant L. Seizures and epilepsy: an overview for neuroscientists. Cold Spring Harb Perspect Med 2015; 5 (6): a022426.