The exact use of such terms depends on context and author, but generally speaking, I would say that concurrency is a much broader term than parallelism; parallelism is a form of concurrency.
The term concurrency is generally used to describe a situation in which processing doesn't necessarily happen in strict sequential order. The things in question can be events, or processes, or actions performed by humans, by computers, by nature, or whatever else ... it really is a very broad term. Examples of concurrent processes:
- a chemical reaction
- shopping at Amazon (including the customer placing an order)
- cars driving around
- you watching a YouTube video
The antonym of concurrency is sequentiality. In a sequential process, everything happens in a strict sequential order: no step starts before the previous step has finished.
The term parallelism is generally used to describe a very specific kind of concurrent process, in which all processing in question is executed by processors within one computer, and multiple processors or threads run at the same time, using shared resources.
The antonym of parallelism is distributed computing; in distributed computing, we still describe processes executed entirely on computer processors, but in contrast to parallel computing, the processors have their own resources, and they need to communicate, usually by means of some form of message passing over dedicated message passing channels, in order to cooperate.
So both parallelism and distributed computing are two specific forms of concurrency, in which all processing is executed on computer processors.
Your question assumes a context in which we're talking about parallelism, and then asks why we use the term concurrency at all, when parallelism will do. Yes, it will, when referring to parallelism; it won't do in general.