Computational Biology and Bioinformatics are the same in a sense that "articulate" and "to articulate" are, which is to say that there is some overlap between their meanings. Yet Computational Biology is a more general term, which is why Statistical Ecology will fall under Computational Biology but not under Bioinformatics.
The National Institutes of Health Biomedical Information Science and Technology Initiative Consortium put out the following definitions:
Bioinformatics: Research, development, or application of computational tools and approaches for expanding the use of biological, medical, behavioral or health data, including those to acquire, store, organize, archive, analyze, or visualize such data.
Computational Biology: The development and application of data-analytical and theoretical methods, mathematical modeling and computational simulation techniques to the study of biological, behavioral, and social systems.
I don't agree completely with their definitions because they don't emphasize the role of informatics molecules (nucleic acids and proteins) in Bioinformatics, but it is a start. I like the definition of Bioinformatics put forth here (full text is here): Bioinformatics is conceptualizing biology in terms of macromolecules (in the sense of physical-chemistry) and then applying "informatics" techniques (derived from disciplines such as applied maths, computer science, and statistics) to understand and organize the information associated with these molecules, on a large-scale. For my students, I sometimes cobble together some of their keywords and shorten this to: studying macromolecules by applying "informatics" techniques to understand and organize the information on a large-scale.
Definitions aside, anything can be learned. People go to medical or engineering schools and later become lawyers, which I think is at least a comparable stretch to switching from the two fields considered by the original poster.