Why do we put labels on people and their activities? I was trained as an ME, but I got a lot of experience with computers that includes both hardware and software. I started when we used punched cards to program an 8K memory machine.
Let's change the focus: Think of a symphonic orchestra. They are to play a work by Beethoven. What is the hardware in this case? It is the instruments themselves. But they have help - the musicians themselves who interpret the music (score). Then, there is the conductor. He/she has the entire score so he can see what each instrument and section must play. His job is to ensure that everybody stays in balance and to manage transitions from one mood to another. Finally, think about the composer. Beethoven had to know and understand what each instrument and musician could do before he put any notes on the staff. In this analogy, I think the musical notation is the oldest form of programming language that ever existed. So, he is the programmer, or software engineer, but he also had and needed extensive knowledge about the software and environment for which he was programming. The amazing thing is that, 400 years later, we can pretty much re-create what Beethoven had in mind when he wrote the piece. And, we can also play it on a variety of different instruments - including keyboards and synthesizers, etc.
Note that this analogy works even for a small group of musicians playing together. They must have a common language that allows them and their instruments to interact.
In today's world, computers control many things and perform many useful tasks in processing data, creating images, etc. So, whether your focus is on hardware or software, the main thing is to consider how your role fits within the overall objective of your organization. If you are a software engineer, you must still understand the hardware available, including the processor, memory, peripherals, sensors and actuators. If your focus is hardware, you still need to understand when and how the software deals with each physical device. In either case - hardware or software - if you don't understand how software and hardware play together, you won't have a very good orchestra performance.