Mark is correct that the two services are very similar, just as you have noticed. If your output is within Synapse, then using Pipelines will be easier unless you need one of the features only available in ADF. The differences are listed here: https://learn.microsoft.com/en-us/azure/synapse-analytics/data-integration/concepts-data-factory-differences
For storage integration with Synapse, you can use either, and which one depends on how you are going to access the data. From the information you've provided, I would choose Data Lake, especially if you think you'll ever need to access the data directly from either SQL or Spark pools within Synapse. Data Lake is built on top of Blob Storage, so there is no difference in the underlying infrastructure. The difference is that Blob storage is essentially a general-purpose storage option, where as Data Lake adds big data optimized drivers, and use Hadoop permissions and access, which pairs better with Synapse pools.