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Yes--these two terms mean essentially the same thing. There might be variation among practicing statisticians and researchers (perhaps geographically, with those in the U.S. preferring the phrase "inferential" and those in other countries perhaps more likely to use "inductive"). The goal of inferential statistics is to make a broader statement about a large group from a small subset of that group--and the phrase "inductive reasoning" refers to making a broader generalization (that is, an inference) from a series of observations. Thus, these two phrases refer to the same thing.
There is no inferential data. There is inferential statistics which from samples, you infer or draw a conclusion about the population. Hypothesis testing is an example of inferential statistics.
Inferential statistics uses data from a small group to make generalizations or inferences about a larger group of people. Inferential statistics should be used with "inferences".
Descriptive statistics is a summary of data. Inferential statistics try to reach conclusion that extend beyond the immediate data alone.
One advantage of inferential statistics is that large predictions can be made from small data sets. However, if the sample is not representative of the population then the predictions will be incorrect.