The two muscles are in contact with each other proximally (close their origin), but diverge distally (towards their insertions).

[1] The sternothyroid muscle receives motor innervation from branches of the ansa cervicalis (ultimately derived from cervical spinal nerves C1-C3).

The sternothyroid muscle indirectly depresses the hyoid bone by means of pulling the thyroid.

When the hyoid bone is fixed, it instead elevates the larynx (producing an increased voice pitch).

This article incorporates text in the public domain from page 393 of the 20th edition of Gray's Anatomy (1918)