On Wikipedia, there is one page for centre-surround antagonism and one for lateral inhibition. They both concern the activity of a neuron being reduced by stimuli present not in the center of its receptive field but near its periphery.
The term 'center-surround' is used specifically for retinal connectivity and visual processing. Specifically, it enhances contrast perception by exaggerating differences in light responses.
Lateral inhibition includes center-surround antagonism observed in the retina, but is a more general term also applied for similar processes occurring in other sensory systems, like the tactile senses.
The two are similar in some ways, but most definitely different in reality. Presenting stimuli near the periphery of a sensory neuron's receptive field (RF) can indeed lead to inhibit its activity (i.e. reduce its action potential discharge rate) through both of these mechanisms, but the mechanisms operate differently.
Centre-surround antagonism is independent from other nearby neurons. If a single neuron were isolated and a stimulus presented in its receptive field surround, its activity would get inhibited.
Lateral inhibition, on the other hand, doesn't talk directly about the RF, but rather about neighboring neurons in the brain. The "lateral" doesn't refer to geometric proximity, but rather to so-called lateral connections (i.e. at the same level of abstraction in cognitive processing) between neurons in the brain.
In truth, receptive fields can overlap, and due to "x-topies" (somatotopy, retinotopy, tonotopy, etc.), both mechanisms can end up active at the same time (but not always!).