A guide to independent contracting, including contract length, definitions, and penalties for misclassification in Ireland.
boundlesshq.com
In general, people on fixed-term contracts have the same rights as employees. They qualify for a redundancy payment if continuously contracting for two years, and they are also covered under unfair dismissal if they have one year of continuous service. A fixed-term worker cannot be treated less favourably than a permanent employee.
The reference to fixed term workers in your link, is referring to employees on fixed term contracts (as opposed to employees with permanent contracts or contract of indefinite duration). I can understand your confusion though Brendan, as it's a very poorly laid out and worded page. It looks like it wasn't written by someone entirely conversant with the vernacular of Irish employment law, otherwise the language wouldn't be so loose.
The longstanding fundamental remains unchanged, that a person is either working under a contract for services (self employed individual in business on their own account), or is an employee under a contract of service.
The potential cost (via employer's PRSI, holiday, sick and redundancy entitlements) means that businesses are extremely averse to accidentally taking on employees. Thus a third possibility has become commonplace in the last 20-odd years, of a layer being created, by the insertion of another corporate entity (be it a personal services company owned by the individual worker, or an umbrella company / managed services company administered by the likes of Contracting Plus).
In substance all that this does is facilitate arrangements being made that mean the party looking to acquire labour / skills / expertise (on terms which would be categorised as an employment / contract of service if the individual was engaged directly), to obtain the services they need without having to take on employees.
By inserting another entity, e.g. Mandelbrot Limited, into the arrangements, they can contract with that company to provide them with the professional services of Mr Mandelbrot in such a way that the only employment relationship is between Mr Mandelbrot and his company Mandelbrot Limited. The end user of Mr Mandelbrot's services simply pay his company the agreed hourly invoiced rate, and most of the various risks / responsibilities as an employer fall on his company. This structure also offers some benefits from the individual's perspective, such as favourable pension planning options.
All of the above is simply a preamble to my main point here, which is that any legal / constructive obligation to pay redundancy can only run from when an individual had an employee/employer relationship with the company terminating them. The whole purpose of the contracting arrangements I've described above is specifically to protect the MNC's and other large employers from such exposure. The hourly rates paid to contractors (via their intermediary entity) are higher than the hourly rate of an equivalent employee for this reason.
In the OP's case here, if they'd been cut loose during, or at the end of the 4-year period as a contractor, there'd be no question that they would have any redundancy entitlements - that's the nature of working as a contractor, and they will have received a higher hourly rate as a trade off for lack of security of tenure.
The fact that they then took on a role as an employee for 4 years, can't somehow retrospectively confer any legal or contractual entitlement to redundancy (unless explicitly included voluntarily in their contract, which would seem daft in the context). The logical (and legal) consequence of the OP successfully arguing this point, would be that their contracting arrangement for the first four years were in fact a sham, and a whole mess of tax and PRSI issues would necessarily follow.