I have a set of 2 ordinal categorial variables and I want to see the relationship between them. Chi square shows a significant value while the spearman correlation is non significant. What does it mean and which test to use to define the relationship better.
The chi-square ignores the ordering in your categories. It will respond to any kind of association between the variables.
The Spearman takes account of the ordering but is responsive to a tendency for monotonic association (when both variables tend to be larger together and smaller together, or when both variables tend to move in opposite directions)
[The usual test of Spearman correlation is really designed for continuous variates; it can be used for the discrete case if the heavy ties are dealt with appropriately.]
If you want to find monotonic association, the Spearman will tend to have much better power than the chi-squared test. If you want to find more general kinds of association, then the chi-squared test will be able to detect associations that the Spearman cannot.
Which you use is up to you -- it depends on what you're interested in looking for.