Here are definitions of the two tests:

The chi-square statistic is used to show whether or not there is a relationship between two categorical variables.

The purpose of the correlation coefficient is to determine whether there is a significant relationship (i.e., correlation) between two variables

I guess that the difference lies in the question whether you data in categorical.

Chai Square test is a non-parametric test -- meant for observed data. e.g., types, categories, varieties etc. The test statisticis is based on Chai-square distribution.

Pearson R or correlation is a parametric test -- meant for measured and recorded in terms of numbers etc. The test statistics is based on normal distribution of the variables.

I agree completely with Avishag.  If both of your variables are categorical, then a chi-square would be more appropriate.  However, both personality and academic achievement are more typically measured as continuous variables, so it’s unclear if chi-square would be best for you.  What are your variables and are they categorical?  Vasulu also makes a good point about another difference between correlation and chi-square.  If your variables are continuous but don’t meet the assumptions of a parametric test, you would probably want to conduct a Spearman rank-order correlation.  Best wishes with your project, Maria! ~ Kevin

I agree with the above. Which test to use depends on the variables you're investigating (nominal, ordinal, interval or ratio. You would use Chi-squared if your variables are nominal. Based on the title of your research, it sounds like you're using some sort of instrument to determine abilities, and so forth. If that's the case, and you're interested in correlating one variable with another, you'd use Pearson r.