Short answer. The Civil Code recognizes three kinds of succession: testamentary, where a valid will governs; legal or intestate, where the law governs because there is no will or it does not dispose of everything; and mixed, where both operate together over the same estate.
What the law says
Succession may be: (1) Testamentary; (2) Legal or intestate; or (3) Mixed.
Civil Code, Article 778 — Three Kinds of Succession. Read the full provision →
Testamentary succession follows the decedent's own will
This is succession that results from the designation of an heir made in a will, executed in the form prescribed by law. The decedent's own wishes, as expressed in a properly executed will, determine who receives what — subject always to the legitime the law reserves for compulsory heirs, which even a valid will cannot defeat, and which limits how freely the decedent could actually dispose of the estate.
Legal or intestate succession applies when there is no valid will covering everything
Where a person dies without a will, or with a will that is void, or that does not dispose of all of the estate, the law itself steps in to determine the heirs and their shares. This is the succession that operates by default, following the order of intestate heirs the Civil Code sets out, rather than any instructions left by the decedent.
This category is often described as the succession the law presumes the decedent would have wanted, in the absence of any expressed wish of their own, and it is the most common way estates are actually settled in practice.
Mixed succession combines both within a single estate
The two categories are not always mutually exclusive within one estate. A decedent may leave a will that validly disposes of part of the property, while the remainder — whatever the will does not cover — passes according to the rules of intestate succession. In that situation, testamentary and legal succession operate side by side over the same estate, rather than one excluding the other entirely, and each separate part of the estate is settled under whichever set of rules actually governs that particular portion.
Why the classification matters
Which kind, or combination of kinds, applies to a given estate determines the framework for figuring out who inherits and how much. A will that is entirely valid and covers the whole estate calls for a different analysis than an estate with no will at all, or one where the will only partially disposes of the decedent's property — so identifying which kind of succession is actually in play is usually the first step in settling any estate, before anyone can meaningfully discuss shares or heirs.