Other-Hearted, also synonymous with Animal-Hearted, is when an individual strongly identifies with a species of creature. It's more than a fascination or like of the creature, like in the furry fandom, but not quite to the point of being something you identify as, like with a therian or otherkin. The creature you feel a connection with will replace the animal part of the phrase. For example, you identify strongly with dragons, you would be dragon-hearted.
There is a thread on AHWW from January 15, 1997 in which someone who claimed to "ABSOULUTLY ADORE WEREWOLVES AND WOLVES" asked if they were "wolfhearted".  The exact terms other-hearted and animal-hearted seem to have come into more common use around 2014 or 2015. Some people may use the term Kith.
The Exact Definition of Being Other Hearted, Calico, January, 09, 2015, The Other Hearts Forum. http://theotherhearts.canadian-forum.com/t10-the-exact-definition-of-being-other-hearted
Other-Hearted vs. Otherkin, Marz, May 4, 2016, Kinmunity Forum. https://www.kinmunity.com/library/information/other-hearted-vs-otherkin-r5/
Otherhearted: What Exactly is Kith?, Renata, March 22, 2016, Therian Guide Forum. https://forums.therian-guide.com/Thread-Otherhearted-What-exactly-is-Kith--3337