The equivalent to "Bachillerato" could be one of the following options: "A-levels" or "Sixth form". British students over 16 typically study in the sixth form of a school, in a separate sixth form college, or in a Further Education College. Students typically study level 3 qualifications such as A-levels, BTEC National awards and level 3 NVQs (National Vocational Qualifications). In Britain, students at this level would be in years 12 and 13, which is key stage 5.
If we want to make a distinction based on the subjects chosen, we could talk about "branches".
Click on the link below to hear how to pronounce these words.