With UK degrees, you choose your major before you begin the degree and you study in just one department for the entire 3 years, with no option to take classes in other subjects unless you are offered the chance to take an elective module in a different department. The first year of the degree does not actually count towards your final degree classification, so although you must pass the first year to continue on to the second year of study, your actual grades won't mean anything for your final degree results. So, the degree is graded entirely on the second year and third year, often split 50/50 or 40/60. The majority of UK degrees involve a year-long research project and dissertation carried out in the third year, although the project title and supervisor are decided during the second year. I did a 4-year undergraduate degree, giving me a masters at the end, and I had to do a 2-year research project - I chose the project title at the end of the second year and handed in my final dissertation at the end of the fourth year.
When you register for the university, you have to register in the fall for an entire year at once, however, you don't register for individual classes - instead you go to your department and they give you a timetable for the semester. Each class is only offered once each year and is only taught by one professor (so no picking and choosing when you will take the class or which professor you want and no missing out on a class because it is full - everyone on a particular degree programme must take each required class). If you fail a class and don't pass the re-sit in September, then you have to repeat the entire year.
As an example of the UK degree structure, here is what my 4-year MPhys Theoretical Physics with North American Study (NAS) degree at Exeter involved:
Before I started the degree, I took 2-year Advanced Level courses in Physics, Mathematics and Geography in high school (approximately equivalent to US AP classes/Freshman year of college). In order to get onto the degree programme, I had to get at least one A and two B's in those three subjects (if I hadn't got at least ABB, I would not have been able to attend the university and would have studied BSc Physics with Astrophysics at Birmingham University instead, which only required grades of BBC).
Year 1 (0% of final degree grade)
PHY1001 Quantum Phenomena
PHY1002 Thermal Physics
PHY1003 Properties of Matter
PHY1104 Fundamental Electromagnetism I
PHY1105 Relativity I and Vectors
PHY1106 Waves and Oscillators
PHY1107 Practical Electronics I
PHY1108 IT Skills for Physicists
PHY1110 Practical Physics I (2-semester class)
PHY1116 Mathematics for Physicists (2-semester class)
Year 2 (25% of final degree grade)
PHY2002 Quantum Physics I
PHY2004 Scientific Programming in C
PHY2006 Fundamental Electromagnetism II
PHY2007 Relativity II and Mechanics
PHY2009 Physics of Crystals
PHY2018 Mathematics with Physical Applications (2 semesters)
PHY2201 Statistical Physics
PHY2205 Analytical Dynamics
PHY2208 Optics
PHY2214 Classical Theory of Fields
PHY3134 Computational Physics
Year 3 (at University of New Mexico, US) (35% of final degree grade)
PHY3201 Advanced Quantum Mechanics (US: 492 Intermediate Quantum Mechanics II)
PHY3202 Advanced Electromagnetism (US: 405/406 Electricity and Magnetism)
PHY3203 Advanced Statistical Physics (US: 505 Statistical Mechanics and Thermodynamics)
PHY3204 Solid-State Physics (US: 430 Introduction to Solid State Physics)
PHY3205 Project: Background Report (5,000 word report for final year project)
PHY3208 NAS Study Elective I (US: 491 Intermediate Quantum Mechanics I)
PHY3209 NAS Study Elective II (US: 327 Geophysics)
PHY3210 NAS Elective III (US: 101 Philosophy)
Year 4 (40% of final degree grade)
PHY3135 Nuclear and High-Energy Particle Physics
PHY3145 Topics in Theoretical Physics
PHY4401 Solid State Physics II
PHY4416 Project (counted for 50% of year - involved a Powerpoint presentation, 3 oral lab-book assessments, a 10,000 word dissertation and a final oral exam)
PHY4428 General Problems (2 semesters)
PHY4432 Relativity and Cosmology