What circumstances causes two different classifiers to classify data exactly like one another
Your results are reasonable. Your data brings several ideas to mind: 

1) It is quite reasonable that as you change the available features, this will change the relative performance of machine learning methods. This happens quite a lot. Which machine learning method performs best often depends on the features, so as you change the features the best method changes.

2) It is reasonable that in some cases, disparate models will reach the exact same results. This is most likely in the case where the number of data points is low enough or the data is separable enough that both models reach the exact same conclusions for all test points.