Finding similar data columns with machine learning
If I'm not mistaken, you are looking for some metrics to investigate if two columns of values represent similar information. Right?

When the order of numbers is fixed for both columns (such that the ith elements of both columns relate to the same record) and hence both columns have the same length, then you can use a wide range of techniques to measure the similarity/distance between the two vectors such as cosine similarity, Pearson correlation coefficient, mutual information, etc.

If the order of numbers in the columns are different or they basically refer to different concepts, then the above techniques are meaningless. In this case, you can look at these columns as two populations of samples. In this case, you may compare their statistical distributions using their distribution parameters (eg mean and std for a normal distribution) or statistical tests (eg ANOVA). In some cases, the number of items (population size) can be different.