Built-in memory belongs to the app. A layer belongs to you.
Products like ChatGPT and Claude ship their own memory, and it is genuinely useful, but it is bounded by the product it ships in, and fragments even inside a single vendor. A memory layer is the same idea pulled out into its own infrastructure layer that spans services, so the memory can move from one app to the next.
The two are not mutually exclusive: a memory layer can complement an app's built-in memory. The trade-off worth naming is that a layer which spans tools also moves your data between them, so it is worth choosing one with controls and privacy practices you trust.