Statistically, we use both terms. I would to like to ask on when we say that's a variable may change over time but this is a parameter which is a constant for a certain time or certain conditions, based on the differences between variable and parameter.
if you go to the favourite links page of my website http://sites.google.com/site/deborahhilton/ there is an electronic statistical textbook, you can word search the two terms, I'm not sure of the answer myself, but I think I've heard people use these somewhat interchangeably although I'm not sure that this is truly correct as maybe they don't define that one should be unchanging and constant http://sites.google.com/site/deborahhilton/
Leaving aside the excellent description @AlexRussell, statistics are inferred by and describe a sample whilst parameters come from a population. In a statistical model, variables are the 'measured' inputs / outputs of the model (alongside with the noise / error) and parameters are the 'coefficients' defined within that model (imagine a model resulting from linear regression). However, for parametric equations, none of what I just mentioned applies (variables may be expressed using a parameter not present in its functional form).
Variables represent that which we intend to model or that which we want to analyze statistically. They can be independent (manipulated in the experiment, predictors) or dependent (measured in the experiment, predicted). Parameters are scalars that determine the effects of independent variables and their interactions on the dependent variable in a mathematical model, or reflect these effects in a statistical analysis.
Consider the general linear model: Y = ax_1 + bx_2 + cx_1x_2 + error. The independent variables are x_1 and x_2, the dependent variable is Y, and the parameters are a, b, and c. Think of variables as the factors in your analysis, the dimensions of your model, the inputs and outputs. You decide what your variables are, and you measure them directly (sample measures). Think of parameters as numbers that "show" how your variables interrelate (population estimates).
Parameter or variable? depending on the view you take. For example, Y= a + b*X. Y and X are usually regarded as variables, a and b parameters. This is correct and clear when dealing one population or one sample. However, when dealing with many populations or samples, a and a should be treated as variables. These variable may reflect the trend among the samples.
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