脖颈 specifically refers to the BACK of the neck (the nape), while plain
脖子 (bózi) covers the whole neck. Note also the colloquial reading
脖颈儿 (bógěngr) with the
儿 suffix, common in Beijing speech.
颈 here is gěng (3rd tone), the colloquial reading; in formal compounds like
颈部 (jǐngbù, "neck region") it's read jǐng.