Is it called just mālā, or does it have a special name? I'm not concerned about the material, rather about the fact that it's shorter and worn on a wrist.
Shiva Purana, 1.25. 29 (The greatness of Rudrākṣa)
śatamekottaraṃ kaṃṭhe bāhvorvai rudra saṃkhyayā | kūrparadvārayostatra ᴍᴀɴ̣ɪʙᴀᴍ̣ᴅʜᴇ tathā punaḥ || 29 ||
"Hundred and one Rudrākṣas shall be worn round the neck; eleven Rudrāksas shall be worn round each of the arms, elbows and wrists."
"This is the rule regarding eleven hundred Rudrākṣas. If so many are not available, another auspicious procedure I mention to you."
Shiva Purana 1.25.34,35:
śikhāyāmekarudrā kṣaṃ śirasā triṃśataṃ vahet | paṃcāśacca gale dadhyādbāhvoḥ ṣoḍaśa ṣoḍaśa|| ᴍᴀɴ̣ɪʙᴀᴍ̣ᴅʜᴇ dvādaśa ||
One Rudrākṣa shall be worn on the tuft, thirty on the head, fifty round the neck; sixteen in each of the arms; twelve round each of the wrists; Shiva Purana
That on the wrist is called as "ᴍᴀɴ̣ɪʙᴀɴᴅʜᴀɴᴀ"
But also one who takes a Vow to wear it are supposed to refrain from :-
madyaṃ māṃsaṃ tu laśunaṃ palāṇḍuṃ śigrumeva ca | śleṣmāṃtakaṃ viḍvarāhaṃ bhakṣaṇe varjayettataḥ || 1.25.43
”A devotee of Śiva shall refrain from eating meat, garlic, onion, red garlic, potherb, Śleṣmātaka, pig of rubbish and liquors."