Understanding students' intentions to study science at upper-secondary school, at university, and to follow science careers continues as a central concern for international science education. Prior research has highlighted that students' science confidence has been associated with their intentions to study science further, although under-confidence and over-confidence (lower or higher confidence than expected, given someone's attainment) have not been considered in detail. Accordingly, this study explored whether under-confident, accurately evaluating, and over-confident students expressed different attitudes towards their science education, and explored how under-confidence and over-confidence might influence students' science intentions. The questionnaire responses of 1523 students from 12 secondary schools in England were considered through analysis of variance and predictive modelling. Under-confident students expressed consistently lower science attitudes than accurately evaluating and over-confident students, despite reporting the same science grades as accurately evaluating students. Students' intentions to study science were predicted by different factors in different ways, depending on whether the students were under-confident, accurate, or over-confident. For accurately evaluating and over-confident students, science intentions were predicted by their self-efficacy beliefs (their confidence in their expected future science attainment). For under-confident students, science intentions were predicted by their self-concept beliefs (their confidence in currently "doing well" or "being good" at science). Many other differences were also apparent. Fundamentally, under-confidence may be detrimental not simply through associating with lower attitudes, but through students considering their choices in different ways. Under-confidence may accordingly require attention to help ensure that students' future choices are not unnecessarily constrained.