Connector or custom
Connector, integration platform, or custom build
A custom integration is not always the right answer, and it should not be the first one considered.
Use the vendor's own connector when one exists and does what you need. It costs nothing to build and someone else maintains it.
Use an integration platform such as Zapier or Make when the logic is simple, the volume is modest, and a monthly fee is acceptable.
Build custom when the logic encodes your business rules, when per-task pricing becomes expensive at your volume, when the integration needs to live inside a system you already run, or when routing sensitive data through a third party creates a compliance problem.