Computer Science vs Software Engineering

I think it depends on the course and the university.

Some "computer science" degrees have large amounts of practical programming and software development.. but others have huge amounts of math content, and much more theory. Traditionally all computer science degrees were mostly math - it's what CS is really about - and that is still the case in a lot of places.

Software engineering in contrast usually is focused on teaching you skills to become a professional software developer. They tend to be more practical and less academic, and probably more likely to land you a job, at least in the places I've worked.

Based on what you've said, I guess you probably would enjoy software engineering more, and it would be more applicable to getting you a job in the industry, but it really depends on the university course you're applying for. Software Engineering at Edinburgh would be much more theoretical than Software Engineering at Brighton, for example.

My computer science course at Sussex university was good, but had courses such as algorithmics (which taught graph algorithms and how to approximate the running times of algorithms) and functional programming - which was mostly math. I struggled at algorithmics majorly, and in some of the math-based courses such as neural computation and advanced neural networks, but in retrospect I'm glad I took the degree. The Sussex degree seemed to have a lot less math content than most other universities around its league table position, so be wary of that.

If you're not strong at math then that won't really stop you having a career as a software engineer, and certainly won't stop you having a career as a web developer (PHP).