An individual school is unlikely to be offering more than one syllabus. They will certainly tailor their teaching to the needs of the individual classes, but need to choose the syllabus and buy the resources for it, well before the students start. So yes, different schools will choose different syllabuses, but are unlikely to offer more than one at A level.
Your child has probably been given the syllabus to put in their file, in the very first lesson. You will be able to see which board they are sitting the exam with and which specific syllabus.
Some schools may also offer some kind of applied science/physics. These courses are usually in less depth, in terms of theory, so may have lower entry requirements. If you are offered a course and told maths is not required for that particular syllabus, I would just ask for confirmation that it is equally valued by universities, to those courses which really do require maths. Again,just worth checking, rather than finding out a year later.
In some subjects such as History, schools may offer several different options from the same Board, to cater to the expertise of staff. So for example, some classes may study modern history and others medieval history. These would be chosen in advance by the school and resourced, long before it was known who would be in the different groups. By the time the students in a set are confirmed (which is really only after GCSE results) it is too late to be switching and changing. Schools build up expertise in the requirements of one board in that subject and do not switch lightly. Whatever they have chosen can be tailored via the teaching to the differing needs of the students, rather than via the course itself.
Of course, if a school has very able students,they might choose a particular course, in the way many schools of this type choose IGCSE syllabus rather than standard GCSE. However, then all of the students will be following that course.