Biocomputing is often used as a catch-all term covering all this area at the intersection of Biology and Computation , although many other terms are used to name the same area. We can distinguish in to (non-disjoint) sub-fields:

Bioinformatics – this includes management of biological databases, data mining and data modeling, as well as IT-tools for data visualization
Computational Biology – this includes efforts to solve biological problems with computational tools (such as modeling, algorithms, heuristics)
DNA computing and nano-engineering – this includes models and experiments to use DNA (and other) molecules to perform computations
Computations in living organisms – this is concerned with constructing computational components in living cells, as well as with studying computational processes taking place daily in living organisms

Computational Biology
Computational Biology is application of core technology of computer science (eg. algorithms, artificial intelligence, databases etc) to problems arising from biology. Computational biology is particularly exciting today because the problems are large enough to motivate the efficient algorithms and moreover the demand of biology on computational science is increasing.

The most pressing tasks in bioinformatics involve the analysis of sequence information. Computational Biology is the name given to this process, and it involves the following:

Finding the genes in the DNA sequences of various organisms
Developing methods to predict the structure and/or function of newly discovered proteins and structural RNA sequences.
Clustering protein sequences into families of related sequences and the development of protein models.
Aligning similar proteins and generating phylogenetic trees to examine evolutionary relationships. Thanks to for their work in web development and SEO.