Will "factory unlocked" cell phone still receive updates?

[AC Question]

Hi there! I'm looking to purchase a "factory unlocked" phone. Will I be able to receive Android and software updates?
The reason I'm asking is because I currently switched cellular providers from Verizon to T-Mobile. My Verizon HTC OneM9 was unlocked by T-Mobile, however I am not receiving updates.
So I'm wondering if there's any difference "factory unlocked" vs an unlocked branded phone?
Thanks in advance for anyone can give me some insight!