“to choke” can be both intransitive and transitive.
intrans.:
“Little Ed gasped, then choked on the half-eaten nuts in his mouth. Françoise thumped him on the back several times until he caught his breath. When he could ...“
„Concerned mum shares how her baby daughter choked on the stuffing of a popular toy. She hopes her warning saves other families. Kath Milroy Pattingale ...“
—intransitive choking doesn’t necessarily lead to death (see first example above).
trans.:
“She choked him with a pillow.”
The intransitive use of “choke” denotes asphyxiation due to an internal cause; the transitive use denotes asphyxiation due to an external cause (e.g., a pillow, or strangulation).
“to asphyxiate” is as far as I know always transitive (or reflexive):
“She asphyxiated him with a pillow.”
“He climbed into his car and asphyxiated himself with carbon monoxide.”
(There are numerous figurative uses of “to choke,” but I guess you’re not interested in those since they have nothing to do with “to asphyxiate.”)