Short answer. A decedent is any person whose property passes by succession on death, whether or not he left a will. A testator is the narrower term: a decedent who left a will. So every testator is a decedent, but a decedent who died without a will is never called a testator.
What the law says
"decedent" is the general term applied to the person whose property is transmitted through succession, whether or not he left a will. If he left a will, he is also called the testator.
Civil Code, Article 775 — Who Is the 'Decedent'. Read the full provision →
The Civil Code's own definition
The Code defines the words rather than leaving them to usage: "decedent" is the general term applied to the person whose property is transmitted through succession, whether or not he left a will. If he left a will, he is also called the testator. Note the structure — one general term, one special case. "Decedent" describes the person by what happened: they died and their property is being transmitted. "Testator" describes the person by what they did before dying: they made a will. The Code even says the testator is also called that — the person remains a decedent; testator is an additional label, not a substitute.
Why the law bothers with two words
The distinction tracks the two ways an estate can pass. When there is a valid will, succession is testamentary: the estate is distributed, within the limits the law imposes, according to the testator's wishes — and the rules speak of the testator because his intentions are what those rules interpret and enforce. When there is no will, succession is intestate: the law itself designates the heirs and their shares, and there are no testamentary wishes to construe — so the rules speak only of the decedent. Which word a provision uses tells you which regime it belongs to; that is why the definitions sit at the head of the law on succession.
Where you will meet the terms
In practice the words appear the moment an estate is settled. Estate tax forms, extrajudicial settlement deeds and court petitions all refer to the decedent, because those processes apply whether or not a will exists. Documents built on a will — a petition to have it allowed by the court, the will itself — speak of the testator. For a family sorting out a death, the practical translation is simple: if your relative left no will, every reference you need is to the decedent and the estate passes by intestate succession; if there is a will, the same person is the testator, and the will must go through the process the law requires before it can operate.