Difference between contract and catch [a disease]

What could be the difference between contracting a disease and catching a disease?

I know there isn't any big difference. However, it looks like there are some diseases you can both catch and contract and others you can only either catch or contract.

While the terms are often used interchangeably with regard to illness, there are some differences.

Contract, in this context, means

[with object] catch or develop (a disease or infectious agent): three people contracted a killer virus

The term is regularly used with chronic diseases:

Women in their 30s and 40s are TWICE as likely to contract cancer than men - with breast cancer largely to blame

Daily Mail

Arthritis: What are the symptoms and who is likely to contract it?

compleatmother.com

Catch means

contract (an illness) through infection or contagion: he served in Macedonia, where he caught malaria

The principal difference is that catch suggests a transmittable infection, while contract can refer to a wider variety of diseases, including those that are not contagious.

contract 3 /kənˈtrakt/ [with object] catch or develop (a disease or infectious agent): three people contracted a killer virus

Use contract in formal or technical English.

Use catch in informal or plain English.

This isn't so much a separate answer as a clarification to the correct answer provided by bib and to answer the comments about contracting a non-contagious disease. I don't have the reputation yet to comment, so I'm putting it in an answer.

Many chronic conditions which should not strictly speaking be called a disease are, in fact, called diseases. For example, heart disease is not something contracted from another carrier like a virus or bacteria, but is instead caused by the combination of factors of genetic predisposition, lifestyle, age, and chance. Yet, one can contract heart disease. One cannot, however, catch heart disease.

If you look in the earlier definition of contract you will see that it has two possible definitions: to catch or to develop.

Also, I think this problem is arising from a shift in the meaning of the word disease. Two decades ago you might have seen heart condition rather than heart disease, but for many of us there is still an implied requirement that a disease be caused by something external, while a condition is caused by something genetic or by lifestyle choice. Forgive me if this observation is too much of a tangent.