Azure Data Lake is a mechanism of data storage. It covers structured and unstructured storage. It’s simply a way to put a lot of data from disparate sources into a single source for easier consumption.
Azure Data Factory on the other hand is a tool for managing data flow and migration. That’s very different.
That’s two different mechanisms, storage and processing.
Azure Data Lake Storage (ADLS) Gen1 or Gen2 are scaled-out HDFS storage services in Azure. Azure Data Factory (ADF) can move data into and out of ADLS, and orchestrate data processing.