In that regard, you would never ask a Mechanical Engineer to change your oil or your spark plugs in the same way you would never ask a Mechanic to design a new high-performance engine from scratch.
Software development is much the same. Computer Scientists (frequently also called Software Engineers) Are concerned with the _mathematical accuracy and precision_ of the software, whereas Programmers are concerned with the _usability and functionality_ of the software. In that regard, they are broadly analogous to my metaphor.
As a web developer, you are a Programmer. Your job is to make functional and usable software that meets requirements. While you can also dive into the structural and philosophical rigour of the code itself, that is not your job. Software Engineers have already trod this path by creating frameworks and patterns and broadly-applicable software development guidelines for you to leverage.
Many places of higher education, however, do make the unfortunate and highly intentional step of muddying the waters and bringing pretty much everything computer-related under the umbrella of “CS”, when most of it is definitely _not_ “CS”. They do so for marketing and income purposes, and in doing so, do a disservice to the industry.