Data Analysts analyze data, assist in finding patterns and build dashboards. Presenting data driven findings may or may not fall under the job descriptions of a Data analyst.
Data Science is about all of the above and more. A Data Scientist uses cutting edge technologies, including but not limited to Artificial Intelligence, Machine Learning, Deep Learning and other statistical & mathematical and big data tools. A Data Scientist is also expected to be well versed and expert when it comes to data engineering.
In plain words a data scientist is a seasoned data analyst. And obviously, a data scientist need to have a PhD. However, there are exceptions.