A simple way to answer is to consider that biostatistics is the application of statistics to biology, while bioinformatics is the application of informatics (which relates to both computer sciences and information sciences... but again to simplify let's consider that informatics is equivalent to computer sciences) to biology. The original question becomes: computer sciences = statistics ? Obviously not, many aspects of computer sciences relate it to logics (e.g. Boolean logics) or electronics (harware)... The difference is now obvious: bioinformatics includes data & knowledge management (databases, ontologies), algorithmic, which are just outside the scope of statistics. In contrast, can be reduce statistics to computer sciences ? Historically, the answer is clearly no... just like mathematics has not been replaced by computer sciences !

Bioinformatics covers a lot more ground than just statistics though. Bioinformatics also includes aspects of data management (storage and retrieval), database design, data visualization (especially important these days when trying to summarize massive data-sets and highly complex analytical outcomes). So it borrows from things like informatics and library sciences as well.

Nowadays, it even can include hardware engineers, as there is a growing trend towards specialized, dedicated hardware for some computations (like image analysis) as well as a growing emphasis on distributed and cloud based systems designed with big data and biology specifically in mind.

I'd say thinking of it as applied bio-statistics is too narrow. There are indeed aspects of bioinformatics that really has nothing to do with statistics. And I know many people whom are considered bioinformaticians yet know very little of statistics. They may be extremely knowledgeable computer coders, database designers, experts at large scale data storage and manipulation. Similarly, many of the statisticians, analysts and computational people I know in bioinformatics settings may know relatively little about application design and development, coding, or informatics of big data.

Bioinformatics in practice covers a very wide range of specialties and knowledge, far wider in practice than I think most people actually realize. Statistics is only one part of it, and more often than not, those with a high degree of knowledge and experience in that one aspect of it, may have relatively little knowledge and experience in other areas of bioinformatics. The reverse is true for many of the people with strong computer science and software development experience, or data management expertise.

That is actually one of the things I love about working in bioinformatics - many different sorts of people can contribute to projects (are needed in fact), each bringing their own expertise to the table without any pretense of being a master of them all (many of the informatics-oriented folks I know in bioinformatics often know very little about biology, for example). Its almost impossible for me to think of bioinformatics other than in a collaborative sense, as by its very nature, the term inherently implies it.

Bioinformatics is a huge domain. As you said it uses part of computer science. In the same way it uses part of statistics too. Without being statistical experts, bioinformaticians should have knowlege in statistics.

To answer your last question, ontologies applied to biology are part of bioinformatics. But, I think, it no need of statistics in such analysis.

Very interesting question. I would rather say bioinformatics is applied part of mathematics (all algorithms used). Biostatistics on the other hand is something parallel to bioinformatics. It is necessary to mentioned however that statistics is everywhere, also in bioinformatics.

I graduated from biology and have bioinformatics as specialization. During my courses I learned Perl, Python and C++ and also about algorithms as BLAST etc. Then I change my interests into more statistical approaches as association studies, regression and analysis of variance studies and a little bit of data mining and machine learning. Machine learning models are sometimes used for gene prediction (Grail software).

So bioinfromatics and biostatistics are sometimes parallel but also some procedures (machine learning e.g. neuronal networks ) are common.

"Biostatistics" is a much older term coined basically for epidemiological analysis (when it was also known as "biometry"). It is represented by the kind of work that Pearson, Fisher, Wright et al (the great bio-statisticians) did starting around the 1920s and 1930s. That term is still used today. However, "bioinformatics", as a much more recent term and that includes all those things mentioned above, will likely subsume "biostatistics" in the end (as it has already done with "computational biology"). In the end, I think the word "bioinformatics" will eventually be used as a very general term to mean all these things (the math-statistics, the computer science and algorithms, the databases and data structures, the networking/storage/transfer protocols, etc)

A simple way to answer is to consider that biostatistics is the application of statistics to biology, while bioinformatics is the application of informatics (which relates to both computer sciences and information sciences... but again to simplify let's consider that informatics is equivalent to computer sciences) to biology. The original question becomes: computer sciences = statistics ? Obviously not, many aspects of computer sciences relate it to logics (e.g. Boolean logics) or electronics (harware)... The difference is now obvious: bioinformatics includes data & knowledge management (databases, ontologies), algorithmic, which are just outside the scope of statistics. In contrast, can be reduce statistics to computer sciences ? Historically, the answer is clearly no... just like mathematics has not been replaced by computer sciences !

Their are a narrow sense and wide sense of Bioinformatics. The narrow sense deal primarily with Sequences analysis. However, after the Genomics era, the bioinformatics includes a wide range of biological data analysis and uses many sciences too