At its simplest:
"Engineering Software" is what people who build software products do.
"Science with a Computer" is something that people doing real calculations, simulations, etc do.
I, too, forget that the tools we use to build complex solutions can still be used by people who don't live in a text editor.
Computer science is the science of computation. It's more to do with theory of computation, information theory, data structures, algorithms, cryptography, databases.
"Science with a computer" is experimental physics, chemisty, biology, etc.
"Computer Science" != "Science with a Computer"
"Computer science" (in contrast to software engineering) is the science that looks into the properties of computers and thing related to it (algorithms, database systems). E.g. examining those systems on a scientific level. Depending on how abstract that can have more or less direct input on how to engineer systems in their software/hardware implementations.
"Science with a computer" on the other hand are usually (in terms of majors/academic disciplines) taught in the adjecent subfields: Bioinformatics, Chemoinformatics, Computational biology, etc.. Of course basic computing is also on some level seeping into every science subfield.