The sadistic Question 4 from the second paper of 2003 invided the candidates to "compare and contrast the use of the Chisquared test, Fisher’s Exact Test and logistic regression when analysing data". This was a terrible idea, and the pass rate was 17%. Such questions have never been repeated since.
Additional reading can be done, if one wishes to actually understand these concepts.
I recommend the following free online resources:
 The Chi Square Statistic from The Mathbeans Project
 Fisher's Exact Test from Wolfram Mathworld
 What is (Multivariate) Logistic Regression from LogisticRegressionAnalysis.com (which is an excellent name).
Additionally, I invite everybody to visit this page, where the author Steve Simon (presumably, somebody qualified in statistics) responds to an email he received which asked him to comment on the differences between a Chisquare test, Fisher's Exact test, and logistic regression.
Qualitiative data types
 Categorical measurements based on descriptions, rather than numerical values.
 Qualitative data comes in two flavours:
 Ordinal data: numerical data assigned to subjective observations, which are ordered (eg. GCS scores)
 Nominal data: Variables described in terms of quality, eg. colour of hair.
 These are tested using the Chisquare and Fisher's Exact Test
Chisquare test
A statistical test commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis. The chisquare test can be used to test for the "goodness to fit" between observed and expected data.
 chisquare is the sum of the squared difference between
observed (o) and the expected (e) data: χ>^{2}= χ(oe)^{2}/e  May be inappropriate if the sample numbers are small.
 Cannot be calculated if the expected value in any category is less than 5.
Fisher's Exact Test
Another test like the Chisquare test, to compare observed data with expected data.
 Used for small data sets (where Chisquare is useless)
 Only applicable in a 2x2 contingency table
Logistic regression
 Method of predicting a binary variable (eg. dead or alive) on the basis of numerous predictive factors, to compare observed and predicted data.
 ICU mortality is predicted using logistic regression analysis
 Regression coefficients allow the contribution of different predictor variables to be analysed.
 Goodness of fit can be estimated using a variety of mathematic methods.
Chi Square  Fisher's Exact Test  Logistic regression  
Application  "give a representation of the likelihood that a given spread of data occurs by chance"  
Specific uses 
Nominal data: large samples 
Nominal data: small samples 
Binary variables 
Advantages 



Limitations 



References
The ideal reference for this is the BMJ, with their combination of rich statistics info and OldWorld credibility. I link to the relevant sections of their Statistics at Square One, by T D V Swinscow.