Is Azure Data Lake HDFS?

No, as the name suggests, Azure Data Lake is a Data Lake whereas HDFS is a file system (Hadoop Distributed File System). From a Hadoop point of view, Azure Data Lake (ADL) is similar to Hive, as in, we can create tables and store data in the ADL just as in Hive. All properties of Hive tables such as partitioning, bucketing, strict/non-strict querying etc. are available in ADL.