Where I live the wording doesn't matter, what matters if you signed an employment contract that states your job is remote, or even a lack of a mention of an office location where you are expected to perform work with an assumption (like the job posting specifying) that the job is remote then it's enough for the job to be considered a remote job. If the employer then tries to alter that without trying to give you some form of compensation, it's considered a constructive dismissal and you'd be eligible for employment insurance.