These words are the adjective forms of paraplegia and quadriplegia, which are the names of medical conditions; both words refer to “paralysis of the arms or legs due to a spinal injury.”
If all four limbs are affected, then the person is a quadriplegic ((quadri- means “four,” such as in the mathematical words quadratic (having four terms) and quadrant (one fourth of an area, originally)).
If a person loses the function of only their legs, then they are paraplegic; para- is a prefix with many related meanings, such as “partly,” “beyond,” “related to,” and “departing from” as in words such as para-sailing, para-normal, para-autistic, and para-psychology. Therefore a para-plegic is a person who is partly paralyzed—specifically in the legs.
Note: Although paraplegic and quadriplegic are adjectives in form, they function as nouns to refer to a paraplegic (person), or a quadriplegic (person).