Spark is an in-memory distributed computing engine.
Hadoop is a framework for distributed storage (HDFS) and distributed processing (YARN).
Spark can run with or without Hadoop components (HDFS/YARN)
Distributed Storage:
Since Spark does not have its own distributed storage system, it has to depend on one of these storage systems for distributed computing.
S3 – Non-urgent batch jobs. S3 fits very specific use cases when data locality isn’t critical.
Cassandra – Perfect for streaming data analysis and an overkill for batch jobs.
HDFS – Great fit for batch jobs without compromising on data locality.
Distributed processing:
You can run Spark in three different modes: Standalone, YARN and Mesos
Have a look at the below SE question for a detailed explanation about both distributed storage and distributed processing.
Which cluster type should I choose for Spark?