At the most basic level, computer science is about creating software—that is, digital systems created using coding languages. Engineering is about creating plans to build physical systems—anything from drones to skyscrapers to medical devices. Computer scientists and engineers often collaborate: for example, engineers will often use the code written by computer scientists to develop a physical system. (It can be a little confusing because computer scientists are often called software engineers.) 

Even within these fields, there are all sorts of specialties. Here are examples of engineering specialties, as described by the Bureau of Labor Statistics:

• Aerospace and aeronautical: for students who are interested in designing aircrafts
• Agricultural: for students who are interested in the technology behind farming
• Architectural: for students who are interested in making buildings
• Biomedical: for students who are interested in engineering as it relates to medicine
• Chemical: for students who want to create processes to produce materials 
• Civil: for students who are interested in the built environment, like bridges
• Computer: for students who are interested in software development and hardware engineering
• Computer software: for students who want to create the software behind most technology
• Electrical and electronics: for students who want to work with electronics and electricity more broadly
• Environmental: for students who want to help solve environmental problems
• Industrial: for students who are interested in creating systems to make people and machines work together
• Marine: for students who are interested in creating technology for ships and boats
• Materials: for students who want to study the properties of and create new materials 
• Mechanical: for students who want to work which mechanical systems
• Nuclear: for students who are interested in working with nuclear energy
• Petroleum: for students who are interested in working with oil and gas

And drilling down even more, here are some examples of computer science careers:

• Software application developer: someone who creates apps
• Computer systems analyst: someone who works to improve broader systems involving computers 
• Web developer: someone who creates websites
• Network systems administrator: someone who supports the computer system for a given organization
• Database administrator: someone who maintains an organization's information databases

Of course, not all of these specialities translate into popular college majors. According to the website Interesting Engineering, the ten most popular engineering majors are as follows (with the schools most known for these majors in parentheses):

• Mechanical Engineering (Georgia Tech, Penn State, and Virginia Polytechnic Institute and State University)
• Electrical Engineering (University of California-Berkeley, University of Texas at Austin, and University of Illinois at Urbana-Champaign)
• Civil Engineering (University of Illinois at Urbana-Champaign, Texas A&M University, and Virginia Polytechnic Institute)
• Chemical Engineering (University of California-San Diego, Georgia Tech, and Ohio State)
• Computer Engineering (University of Illinois at Urbana-Champaign, Ohio State, and Georgia Tech)
• Biomedical Engineering (Georgia Tech, Arizona State University, and Boston University)
• Industrial Engineering (Georgia Institute of Technology, Purdue University, and the University of Michigan)
• Aerospace and Aeronautical Engineering (Embry Riddle Aeronautical University, Georgia Tech, and Purdue University)
• General Engineering (Arizona State University-Polytechnic, University of California-Davis, and East Carolina University)
• Petroleum Engineering (Colorado School of Mines, Texas A&M, and Penn State)

You'll notice that most of the schools listed are large universities, so if your student is interested in engineering or computer science, they will likely gravitate toward these bigger schools, many of which are tech-specific institutions. Of course, that doesn't mean a student can't study engineering at a small liberal arts college, but they will likely be able to focus more intensely at a school with a stronger specialization.