Both core and comparative texts may be used throughout your course of study. Though it may seem that the differences are few and possibly inconsequential they are there for a reason.
Core texts are specified by exam boards for study, i.e. they are what they deem to be of importance within the context of the study of English Literature. They are often well-known texts that have been studied by students year upon year and have been chosen by the exam boards to coincide with paricular units. For example, if one of the units being studied were 'The Supernatural' a core text would more likely be Wilde's 'The Picture of Dorian Gray' rather than Austen's 'Mansfield Park' (though this example is fairly base).
Comparative texts, in contrast, may be used to further a student's knowledge of the canon of English Literature in its entirety. For instance, carrying on from the example previously presented, it may be recommended that the student read Shelley's 'Frankenstein' or Carter's 'The Bloody Chamber' in conjunction with 'The Picture of Dorian Gray'. Aleternatively, comparative texts may be used within an exam or essay to highlight differences within particular traditions of Literature. This enables students to further their understanding of techniques used by authors and how these may acheive simailar effects, though on the surface they may differ. It is of importance to use both core and comparative tets, particularly at this level of study in order to ensure a well-rounded understanding of what may be being studied.