In the Tantrik scriptures and terminologies, Klim is widely known as the "kAma vija", which is associated primarily with Lord Krishna. On the other hand, Krim, known as the "sharmada vija", is associated exclusively with Goddess KAli. Krim is known as the KAli Vija and Klim the KAma Vija or Krishna Vija.
There is a Tantra, called the VaradA Tantram, which gives the expository meanings of the various Vijas (like aim, hrim, haum, shrim, dum, gam etc., etc.) in the Patala 6 of the text, by breaking down the letters, mAtrAs found in a particular Vija.
The verses I quote below are given in the book "Anhika Krityam - by Shyamacharana Sharma AKA Shyamacharana Kaviratnavaridhi", 1st bhAga, 1st khanda (on p.79):
Klim (KAma)--- Ka kAmdeva uddishtohapyathava krishna uchyate |
ee tushti-vAchi sukha-dukkah-pradancha ||
ka --- kAmadeva or krishna; la --- Indra; symbolic here of opulence or
Aisharya; ee --- Tushti or appeasement or pleasure; anuswara --- giver
of happiness and destroyer of miseries.
Over all meaning --- Let the opulent kAmadeva or Krishna provide me
with pleasures and happiness and let him remove my miseries.
Krim (Sharmada) ---
ka kAli brahma ra proktam mahA-mayArthakashcha eeh |
viswa-mAtArthako nado vindur-dukkha-aharArthakah ||
ka --- kAli; ra --- brahma (supreme reality); ee --- mahAmAyA (the
great enchantress); nAdA --- viswa-mAtA (world mother); bindu ---
dukkha harana (removal of miseries);
Overall meaning --- Let, the mahAmAyA, Brahma-swarupa, Jagajjanani,
Goddess KAli remove all my miseries.
Aspirants, who are initiated into KAli mantra, sip water during Achamana, using the mantra Krim. So, Krim is obviously important in KAli-Kula. Klim, on the other hand, is a generally important Vija, that is found in mantras of various deities, but is primarily associated with Krishna.