Strong Spitters are an evolution of the Spitter.
Strong spitters act similarly to spitters, attacking Albert West with projectiles (that slow West) whenever he is close enough, and attacking with their claws if he is too close. Unlike spitters, strong spitters will try to get as close as possible to West, spitting at him whenever possible.
Like the spitter, an accurate gun is a safe option to kill strong spitters, but close-ranged combat is an alternative, especially if you can react quickly. While strong spitters have more health and deal more damage than spitters, they begin spawning later in the game than spitters, which should give you more time to get better equipment (or get used to the game).