If one were to say "I entered my apartment building", does that mean that:

• the building contains the speaker's apartment (which belongs to him/which he holds on lease); or
• that the ENTIRE building belongs to such person?

I'm assuming that it's mostly always used to mean the former. However, is there a way to properly distinguish between the two in American English?

For example, is using the below two phrases more accurate & idiomatic?:

• "my apartment's building" for the former; and
• "my apartment building" for the latter.