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Integration
An integration is the specific way one of your apps uses a connection, for example, syncing Google Contacts into a people database.
A connection is the account or tool itself, GitHub, Slack, an API key. An integration is the decision about how a particular app puts that connection to use: what gets pulled in, what gets pushed back out, and on what schedule.
Assistant
Integrations and connections are deliberately two different concepts. You can have a GitHub connection with no integrations using it yet, or one connection powering several different app integrations at once.