Fixtures are items that are attached to the leasehold property. Example: A built-in cabinet that is affixed to the wall is a fixture; a stand-alone bookcase is not a fixture.
Disclaimer: This post does not constitute legal advice and does not establish an attorney-client relationship.
The tenant improvements you mentioned - HVAC, walls - are usually distinct from furniture and equipment because they're attached to the premises and are considered non-removable fixtures when the tenant vacates.
If the kind of improvements you paid for are particularly portable, you may be able to argue
that they're not fixtures and belong to you and can be taken when you leave.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
A classic example of fixtures are lighting solutions that are "attached" to the walls. One thing all tenants should recognize is that many leases expressly call for the fixtures to become the Landlord's property following surrender of the premises (or for the tenant to remove them at his/her expense within a certain timeframe). You should bear this in mind before embarking on any major build-outs or rennovations to the premises and/or consult ahead of time with the Landlord regarding the fate of certain fixtures post surrender.
I hope this helps.
Disclaimer: This answer is for informational purposes only and does not constitute general or specific legal advice, nor create an attorney client relationship.