For what it's worth, based on my experience working in the tech (software) industry in the US for the past decade, "be engaged" or "get engaged" is used by management to mean "actively participate in something". If anything, it's an even stronger way of saying "be involved" to those folks. To be involved in something runs the gamut from "merely going along to watch" to actually being the main driver or star behind a project. But when your manager asks you to get engaged in a project, they're thinking of a much smaller range of activities all of which imply that you're playing an important role in the success of the project. I agree that "engaged" *can* also mean "paying attention" to something. But that's not its only use, and the number of times I've heard it used to mean that is probably in the minority. P.S. there's "engage in conversation" which implies interaction (which is activity), and "engage the clutch" which means that the engine is directly connected to the wheels, which also implies a sense of the dynamic.

As Julio already stated, "being involved" means becoming part of something, whereas "being engaged" means you're simply aware of something. For example: "I am involved in class." This means you're consistently participating in classroom activities. "I am engaged in class." This means you're attentive in class: you listen to the teacher, you understand directions, etc. I hope this was a helpful answer. Please feel free to ask any questions you may have.

Being involved is being a part of something. Being engaged is more for paying attention (or when someone proposes to you and you say yes , you guys are engaged) .