is there really a difference among programmers, software developers and software engineers?

In broad terms not really

Depends on the branch of study I suppose. My degree says I'm a software engineer and because of the broad spectrum of development practices from code to project management and design. A computer studies student may have a slightly narrower field etc... The terms you use can describe anyone in the field thb

@willywos can't upvote you enough for that comment

There is a slight difference between programmers and software engineers: Programmers are responsible for translating someone's designs into code, while software engineers basically ensure everything is working properly.

@Nojil sorry but that statement about software engineers is totally inaccurate

It's a super generalized statement :) I don't expect it to fit every role

@Nojil there isn't a generalisation, software engineer has a specific meaning