Proximal is an adjective that describes something or someone as near something else, or nearest a central point. In this sense it is a synonym of proximate.
However, both words have other definitions that make them distinct.
Proximal is often used in medical and dental fields. If something is proximal it is near the center of the body (as opposed to distal). Each tooth has a proximal surface. The adverb form is proximally.
Proximate can carry a causal definition, that because one thing is proximate to something else it has a clear relationship. The adverb form is proximately. The noun form is either proximateness or proximation, with the latter being the preferred.
UEX’s Hidden Bay Project is located in the eastern Athabasca Basin and is proximal to several of the region’s major uranium deposits and mines. [CNN Money]
“It is this “clean cut” [which is] the key to spinal cord fusion, in that it allows proximally severed axons to be ‘fused’ with their distal counterparts.” [SBS]
Since the pipeline and ports would operate proximate to vital economic and environmental spaces on the U.S. border, such as the Great Lakes and Atlantic coast, any oil spill would still impact the health and earnings of American citizens. [Forbes]
“Plaintiff received no warnings prior to the incident and was without fault,” the suit states. “Plaintiff’s slip and fall was proximately caused by the negligence of defendant.” [The Southeast Texas Record]
Given his prior exposure, he was the typical Europhile, committed to a vision of Africa’s “progress” defined by proximation to western standards of doing things and thinking. [All Africa]