Translation guide
The English word "stalk" has two main meanings: the stem of a plant, and the act of following or harassing someone. These meanings are completely separate in Japanese.
The main stem of a plant, leaf, flower, or fruit.
To follow someone persistently and obsessively, often in a threatening way.
The most common way to say "to stalk" someone, using the loanword "stalker" as a noun and adding "行為をする" (to commit the act).
The plant meaning and the following meaning are completely unrelated in Japanese. Using 茎 (kuki) to mean "stalk someone" would be nonsensical.
つきまとう is a broader term for following someone around persistently, which can include stalking but also less severe behavior. ストーカー行為をする specifically refers to the crime or act of stalking, often with legal implications.
Please chop the celery stalks.
Often used for the central stalk of a leaf or feather, or the axis of a plant.
The leaf stalk is broken.
He was arrested for stalking his ex-girlfriend.
A native Japanese verb meaning to follow someone around persistently, often with a negative connotation. It can be used for stalking or just being a nuisance.
A strange man is stalking me.
The verb form of "stalking," used as a suru-verb. Less common than the noun phrase, but understood.
She is stalking him on social media.
Means "to track" or "to pursue." It can be used for stalking in a more literal sense of following someone's movements, but it lacks the obsessive/harassing nuance unless context is added.
The detective stalked him to get evidence of the affair.