Modern Concept of a Project
Project today refers to any organized (i.e., with a clear distribution of authority to manage labor and capital) effort/endeavor/resource expenditure of some team (organizational unit) to achieve a goal, including the goal of creating and developing a system (including system usage), i.e., "managing the life cycle" as stages of conception, creation, operation, and decommissioning — and so on with many versions and even individual features of the target system.
Today, the word "project" is not exclusively associated with "a project in classical project management practice," that is, how the concept of "project" is defined in the associations of project management such as the Project Management Institute (PMI), PRINCE2, and the like. A project can also refer to a case of fixing a leaking toilet in the office, a programmer's three-month effort using the SCRUM method, which did not involve Gantt charts at all (but instead involved delivering a minimum viable product (MVP) a month after the start, a second version of the MVP a couple of weeks later, and then a major pivot with a complete product rewrite a week later), or even a singer working with a producer (where the singer can easily be replaced without renaming the project), because the producer creates and develops the singer, the target system (the "singer development project" becoming the "singer project" is a language feature, metonymy). Even programs in classical project management (i.e., the many projects generated as the necessity within a "program of projects" is realized) are often referred to as "projects" today. One might say "the moon landing program" to encompass all the projects related to human flights to the Moon, including projects not yet identified as necessary, or one might say "the moon landing project."
Sometimes, instead of "project management," people refer to "work management" and "task management" to distance themselves from classical project management practices and emphasize the free use of the word "project." In any case, it is about "managing work in projects, which are understood in many different ways." Thus, "project" increasingly simply denotes work by an organizational unit to achieve a goal. Therefore, "project" does not necessarily have to be taken as a concept from the body of knowledge on project management in a classical sense. Therefore, the term "project" is often synonymous with the concept of a "case" (work that is needed to transition an object of the case/work product from one initial state — where the case is opened — to some final state, after which the case is closed).
In Russian, there is also a distinction between design and project. Usually, product is the embodiment of the target system in its environment, while project is the system for creating the product, the organizational unit (a group of people organized to create and modify the product). But there is a variation where product is the embodiment of the target system in its environment, while project design is the description/system definition of this product. Sometimes these meanings can be somewhat separated if one pays attention to the verbs: in the Russian language, "a house project" would often be considered design, while "a house creation project" would be considered project.
Reminder: "He was mowing using a scythe with a crooked handle on the meadow" — the brain copes well with homonymity, the same term can mean completely different concepts. Pay attention to the types of concepts (develop your "type machine"), and you will not get confused! "Project" can be anything, pay attention to the type!