No, Computer science and engineering both study how information is processed and transmitted, but the fields are very different in terms of the level of mathematics they employ, their preferred application domains (computer science tends to be more theoretical while engineering is often applied), and what skills they emphasize (engineering majors usually take a lot more physics courses).
A computer scientist will think about computation in an abstract way while an engineer will design a specific process or system to do something. An engineer might design an algorithm that converts PDFs into HTML while a computer scientist would come up with general principles for such conversions without thinking too much about how it’s implemented.
Computer scientists build models of systems, engineers build systems themselves.