You obtain data that is a sample from some population. Your aim is to infer about some properties of the population, given your sample. Alternatively, you may want to learn how to predict behavior of the population, given your sample. So (1) is sample (this is how statistician would call it), or simply data, sometimes also called as input data, or simply input. Next, you take samples from your data and divide it into (2) training (or train), (3) validation and (4) testing (or test) samples (this is what statistician would call them), or sets (this is more informal, since in mathematics set is a collection of distinct objects). Next, after you trained your algorithm, you can make (5) predictions. Notice that predictions are not data unless you want use it as input to another algorithm and learn something from it. Data is something that brings you information and your predictions are just educated guesses, so unless you want to learn something about the educated guesses themselves, this is not "data".