In the software industry and related domains in other industries (i.e. software at a bank, software for retail systems, etc.) the words engineer, developer and programmer can be used interchangeably. I think "engineer" is more trendy these days than "programmer". Other industries also use the words "architect" or even "sanitation engineer" and they mean different things.

I don't think its a big deal that the same words are used in job titles in different industries. The second anyone reads the job description or follows up with a question will understand the domain someone works in.

I usually go with "I work in software" and non-software people equate all of that to "IT", much like I classify Doctors as "medicine" and there are different disciplines.