Do 'Sprint' and 'Phase' in project management define the same concept or do they explain 2 different concepts?
Short Answer: Generally no.
Longer Answer: "Phase" is not a defined term in Scrum, while Sprint is very strictly defined. A Sprint is a timebox -- a 1-4 week period in which work is done. Sprints always end, and Sprints always have certain ceremonies around them.
Phases can mean different things to different people. Some organizations use a "phase" to delineate a version or release. Others define it as a large set of tasks that must be done before moving onto the next set. Yet others see it as a set time limit. So phases can correspond with Sprints, but generally the two terms are not the same.
The term "sprint" comes from Scrum. It is that process framework's term for a timeboxed iteration. A sprint begins with a planning session to review a queue of work (in Scrum, the Product Backlog) to estimate tasks and determine what work will be done in the timebox. The purpose of a Sprint is to produce a potentially shippable increment of software that adds new capabilities and/or solutions to problems delivered in previous increments. At the end, the work done is demonstrated and the team reviews the methods to improve.
I've typically seen the word "phase" used in the context of "phase-gate" or "stage-gate" processes. A phase is a collection of activities that take some kind of input and create outputs by transforming the inputs or creating new outputs. The gate part refers to deciding if the project should continue based on what has been learned or done in the previous phase or if the artifacts produced in the phase are sufficiently stable to do further work with.
I suppose that you can refer to a Sprint as a phase. It has inputs (a prioritized Product Backlog), activities (a Sprint Planning Meeting, a Daily Scrum and daily work, a Sprint Review, and a Sprint Retrospective), and outputs (a Potentially Shippable Increment, updated Burn-Down Chart, updated source code and unit tests, updated documentation). However, I don't think I've ever seen it referred to in that way, simply because "phase" evokes the idea of a more plan-driven methodology.