Yes, no, kind of.

They're both names for essentially the same Royal dynasty, named after Geoffrey V of Anjou, who had a "planta genista" (a plant currently known as the common broom) as his emblem.

Geoffrey's son Henry II was King of England, but also inhereted and married into quite a lot of French territories. Together, this is known as the Angevin Empire. It lasted until the death of Henry's son John I.

Some historians use the term Plantagenet for the entire dynasty from Henry II up to Richard III. Other historians use the term Plantagenet only from John I's son Henry III onwards.

The term Angevin is usually reserved only for the rule of the kings Henry II, Richard I, and John I, who actually ruled the Angevin Empire.

"Angevins" is a French term which design all people living in or around the city of Angers. IT can also be applied to people coming from this area but living elsewhere when they keep a link with their home area. This term is still used currently in France.

The Plantagenets are member of a noble house which was orinigally count of Angers (so at this time because they lived in their castle in Angers, they were angevins). Some members of this family became really powerfull and even King of England