You can apply software engineering to develop an application, but you can also do application development without any proper software engineering.
Software Engineering is a design discipline, management discipline, and engineering discipline. Application development is (principally) the act of building an application by writing code. It doesn't require design, management, or engineering discipline to accomplish. But it's better if you've done those things (minimally, the engineering and design portions).
At the same time, a junior software engineer may not be responsible for anything but the writing of code, where others have determined the design and engineering aspects and are conducting project management for them. Or with only limited responsibility (such as developing tests for the aspects they're responsible for developing, which is a part of the engineering discipline: V&V).
In practice, the main difference is the pay / relative "rank" within a company. Employer's perspective: Want to hire a software engineer but don't have the budget? Create a new role, call it something else, now the pay difference is justified.
Context - I'm a software engineer by title but my job is application development. Which is hard, mind you! It looks like simple coding but it involves prioritizing, making smart decisions, and making all stakeholders happy.
I've worked in both of those environments, where my titles were literally "application developer" and "software engineer". In the former, we did a lot of things without process and worked on a wide variety of applications and in the latter I worked in an Agile environment focusing on a core product.
As with most HR departments, it could be a classification required for salary, which also highly depends on work experience and not necessarily school background.
- Someone who's job title is much fancier than otherwise necessary
Software Engineering is a design discipline, management discipline, and engineering discipline. Application development is (principally) the act of building an application by writing code. It doesn't require design, management, or engineering discipline to accomplish. But it's better if you've done those things (minimally, the engineering and design portions).
At the same time, a junior software engineer may not be responsible for anything but the writing of code, where others have determined the design and engineering aspects and are conducting project management for them. Or with only limited responsibility (such as developing tests for the aspects they're responsible for developing, which is a part of the engineering discipline: V&V).