For the purposes of determining tax and employment rights, we can be employed or self-employed or even both. Unfortunately, there is no simple way to determine our status as it is based on the terms of our contract with our client.
Our intentions are not considered in determining our status. Neither are the intentions of our client. Even if we write our intentions explicitly into our contract they are not used to determine our status. The terms of our contract, and only the terms, determine our status.
Our status can vary with different clients, different contracts with the same client, or even different parts of a single contract.
And, to further confuse the issue, if I form a company I can employ myself thus being an employee for tax purposes but still a contractor to my client.