Of course. You've differentiated the two already by describing two mutually exclusive processes. If you're looking for terminological differences that delineate theory along this distinction, it seems you're looking to distinguish perception from cognition as it exists and operates independently from the direct influence of sensation. Plenty of cognition does not involve sensation or perception directly. Metacognition is a sort of self-perceptive process that operates apart from sensation in the traditional "five senses" sense, but not all cognition even involves self-perception or conscious awareness of the cognitive processes in question. This may be debatable, but I would call perception a special case of cognition – i.e., cognition is the broader domain of mental processes that subsumes perception, but does not always involve it.
One might also argue that you've only described sensation in your first sentence, not perception. Perception refers more directly to the processing of sensory information that the brain has received, whereas sensation refers to all processes leading up to sensory information processing. Thus sensation may include the process of delivering sensory information to the brain, depending on whose definition you subscribe to. Cognitive processes only enter the equation once the information has arrived, because cognition refers to the processes carried out by the brain – mostly the higher processes, so (again, maybe this is debatable) not even what happens in the rest of the central nervous system. E.g., the optic nerves feed cognitive processes, but do not carry out cognitive processes themselves.
Summary: If your first sentence only refers to raw sensory information being conveyed to the brain before the brain does any work to process this information, then I don't think it describes cognition at all, whereas the second sentence describes cognition directly. If you mean to include the brain's interpretive process in the "receives information" step of the first sentence, then it describes perception, which is only one kind of cognition (or maybe also distinct from cognition by some definitions).