Jisho

The Japanese verbs 放つ (hanatsu) and 放る (horu) both relate to the concept of releasing or letting go, but I believe they have different nuances and usages.
放つ (hanatsu):
Meaning: To release, to let go, to set free.
Usage: This verb is often used in contexts where something is being released in a more intentional or deliberate manner. It can also imply a sense of liberation or sending something off.
Example: 鳥を放つ (tori o hanatsu) - "to release a bird."

放る (horu):
Meaning: To throw, to cast away, to let fall.
Usage: This verb is typically used when referring to throwing or discarding something. It has a more physical connotation compared to 放つ and can imply a lack of care or intention in the act of releasing.
Example: ボールを放る (bōru o horu) - "to throw a ball."
So, while both verbs involve the idea of releasing, 放つ (hanatsu) is more about intentional release or liberation, whereas 放る (horu) focuses on the act of throwing or discarding something. At least, that's what I think as a beginning learning of Japanese