In High School I had conversations with my dad about what I wanted to be on the other side of College. We talked about various career tracks and tried to figure out jobs and income opportunities. I thought "systems analyst" sounded cool... I really didn't know what that meant (and still wouldn't if it weren't for wikipedia). In the end, I wanted to know how to build an amplifier and a computer so a double major in Electrical and Computer Engineering seemed the best fit.
In College before I started working as a co-op I really didn't understand various engineering rolls and what they meant. All of the job roles have unique benefits and all are necessary for a product to succeed.
Test Engineer: Responsible for evaluating a companies products in volume(when the company starts making thousands of units) and taking the projects to full production volume(millions) and maintaining production test. As a test engineer you get to work with assembly lines, robots, and often provides instant gratification. The tests you develop are typically immediately running in the real world where you can see the results of your work. Test engineers provide feedback and input to the product and design engineers when potential problems are identified.
Applications Engineer: Responsible for helping customers properly use a product. They get to know the whole system picture for a part or product. Applications engineers are usually responsible for writing data sheets and other documentation that is released to the public. Typically the applications engineer will work with a product engineer during product release. There are various application engineer roles also, a system application engineer will work with customers to define the system(complete picture) specifications(lots of figuring out the nuts and bolts logistics). The system applications engineer provides the specifications of a complete picture (like the total workings of an iPhone) to the design team.
A field application engineer will travel to customer sites and help trouble shoot customer designs as well as provide suggestions for future products along with the system applications engineer. If you want to travel a lot, consider field applications.
Product Engineer: Responsibility varies between companies. In some companies a product engineer is responsible for the entire product life cycle from design verification through volume ramp into sustainment and then end of life. Depending on the type of product a product engineer may have several different products they are responsible for. In other companies a product engineer is responsible for the validation of a product as soon as the design engineer finishes. When the part or system comes back from manufacturing the product engineer runs all the tests to find out what might need to be improved before release.
Design Engineer: Is what it seems like you go to school to learn how to do... design things. A design engineer sits at a desk all day long(8+ hours) and solves problems. A design engineer is likely going to be using computer aided design for the actual design. It may be years before there is a a real product that they can put their hands on. Design projects can also get canceled and a years worth of work is now only relevant experience, not a tangible result to hold in hand and show your family and friends. The amount of "ownership" and responsibility a design engineer depends on the size of the project, the size of the company and the experience of the design engineer. At a startup, a design engineer will likely be responsible for every part of a design and the test and debug of the design normally done by a product engineer. In a large company even an experienced design engineer is likely to be responsible for a single small building block of a large system. Every group is unique and ownership varies drastically even within the same company.
Technical Marketing: Marketing is an extremely important role in an engineering firm. Marketing is what connects the business to the customer so the customers know what a company has to offer. Marketing is more than just advertising. Marketing works with the customer and does industry analysis to determine what the customer needs are. A marketing engineer will work with the systems application engineers and the design engineers to develop product road maps. Marketing is also who takes people out to lunch and various other perks.
Business travel is very different than traveling for vacation. Most of the time you are working the entire time and will only see the Airport, the place you are working, the Hotel and the area's during the commute between these places. It's possible to extend a stay over a weekend, but traveling can also mean being in a different city every other day of the week. Jet lag becomes part of life.