There are several legal concepts going on in your question here, all of which are relevant to the answer:
- separate legal entities
- privity of contract
- novation of contracts
The answer to your question is it depends on the law of governing the contract.
Each State in the US (California, New York, Georgia, …) and each country in the EU (England, France, Spain, …) has its own system of contract law.
Each contract that you refer to in your question might be governed by the law of a different country.
Separate Legal Entities
In HL Bolton Engineering Co Ltd v TJ Graham Sons Ltd 1957 1 QB 159, Denning LJ described companies like this:
A company may in many ways be likened to a human body. It has a brain and nerve centre which controls what it does. It also has hands which hold the tools and act in accordance with directions from the centre.
Some of the people in the company are mere [employees] and agents who are nothing more than hands to do the work and cannot be said to represent the mind or will. Others are directors and managers who represent the directing mind and will of the company, and control what it does.
The state of mind of these managers is the state of mind of the company and is treated by the law as such.
The hallmarks of a separate legal entity are that it can:
- buy, sell and own property of any kind in its own name
- agree to legally binding contracts, and
- sue and be sued in its own name.
Privity of Contract
The doctrine of privity of contract consists of two general rules, one of which is:
- a person who is not a party to a contract cannot sue on the contract to obtain the promised performance.
There are exceptions to privity of contract in some countries’ systems of law.
Novation of Contracts
There is no such thing as an assignment of a contract.
It was held in Linden Gardens Trust Ltd v Lenesta Sludge Disposals Ltd 1993 UKHL 4 (22 July 1993):
It is trite law that it is, in any event, impossible to assign "the contract" as a whole, i.e. including both burden and benefit. The burden of a contract can never be assigned without the consent of the other party to the contract in which event such consent will give rise to a novation.
Although it is true that the phrase "assign this contract" is not strictly accurate, lawyers frequently use those words inaccurately to describe an assignment of the benefit of a contract since every lawyer knows that the burden of a contract cannot be assigned.
In short, contracts are not assigned:
- ownership of assets is assigned.
- contractual rights are "transferred": they're novated.
The legal obligations under a contract cannot be "assigned" or transferred to another person, without agreement from the other contracting party(ies).
To transfer (or “assign”, which is a misnomer) contractual obligations the requirements of novation must be satisfied.
In novation, there is no assignment of rights and obligations: a new contract is created with new rights and obligations, with a new contracting party.
Sales of Companies
So, to answer your question, what sometimes happens is the buyer of Company A (ie Company C) puts the contracting parties of Company A on notice that Company A has been acquired and that Company C will now be fulfilling Company A’s contracts.
Is that an “assignment” of the contract?
Well no, but of the contracting parties of Company A then order products or receive products from Company C, and everyone is happy.
The contracting parties to Company A could say to Company A “You’re in breach of contract for not performing my contract. I can sue you for my loss, caused by your non-performance of the contract”.
Company A could then say, “Well that might be the case, but then you need to mitigate your loss for my breach of contract. There’s a company over there called Company C that can perform the contract that we used to have together on the same terms with you.”.
In respect of your reference to Company AC, please see the heading "Separate Legal Entities" above. As I understand it, there is some sort of doctrine of merger of companies in some States of the US (such as Delaware, I believe), but I don't get into that here, because I'm not a US lawyer. That doctrine of merger might be relevant to the answer to your question under the law of some States of the US.
To an English contract lawyer, going by what you say in your question, Company AC is a trading name of Company C (or vice versa) or Company C changed it's name to "Company AC".
It might work differently in the governing law of the share purchase agreement or asset sale agreement.
If you’re thinking of relying on any of the above for an actual acquisition, please seek medical help.