What is the difference between the theories of evolution by natural selection and intelligent design?
The theory of evolution by natural selection is a scientific theory that explains how species change over time through the process of natural selection. It proposes that organisms that are better adapted to their environment are more likely to survive and reproduce, passing on their advantageous traits to their offspring. This theory is supported by a large body of evidence, including fossil records, comparative anatomy, and genetics.

Intelligent design, on the other hand, is a belief that certain features of the natural world are best explained by an intelligent cause rather than natural processes. It suggests that complex biological structures and processes, such as the human eye, are too complex to have evolved through natural selection alone, and must have been designed by an intelligent being. Intelligent design is not considered a scientific theory because it is not testable or falsifiable through empirical observation and experimentation, and it relies on supernatural explanations.

In summary, the main difference between the theories of evolution by natural selection and intelligent design is that evolution is a scientific theory supported by evidence, while intelligent design is a belief that relies on supernatural explanations and is not considered scientific.
What proofs and/or hypotheses do either side present for their case? Give me a couple of examples of famous people (scientists, celebrities, athletes, politicians etc.) who support either side and if you can access their arguments for this.
The theory of evolution by natural selection is supported by a large body of evidence from various fields of science including paleontology, biogeography, and molecular biology. For example these include
 
1. The fossil record which shows a progression of changes in species over time, 
2. homologous structures which are similar structures found in different species that suggest a common ancestry, and 
3. DNA evidence which shows similarities in the genetic code of different species

Conversely, the proponents of intelligent design argue that certain features of the universe and living things are best explained by an intelligent cause rather than an undirected process such as natural selection. Some arguments for intelligent design include

1. the complexity of biological systems which they argue could not have arisen through natural processes, 
2. the fine-tuning of physical constants and laws that allow for life to exist, and 
3. the existence of information in DNA

The majority of scientists are convinced by the evidence pointing to theory of biological evolution. To name one: Charles Darwin, a British naturalist who first proposed the theory of biological evolution by natural selection. On the other hand, there are several notable scientists who support intelligent design including Dr. Brian Josephson, a Physics Nobel prize winner.