Is ensemble learning using different classifier combination another name for Boosting? For implementation I am following the Matlab code for AdaBoost. Based on my understanding, AdaBoost uses weak classifiers known as base classifiers and creates several instances of it. For example, a weak classifier is a decision tree. So, AdaBoost can create maximum N decision trees (where N = number of samples) and combine the prediction results. This is a Homogeneous boosting method. But I have seen some examples such as this one in Matlab and ensemble-toolbox which have confused me. Can somebody please explain the following concepts with respect to the implementations and what is going on in the code?

1) Does the Matlab code for AdaBoost combine different classifiers? The combination method is unclear to me - -whether they do sum or majority voting or something else.

If they are combining several classifiers, then technically it is a Heterogenous ensemble method and the term for it is stacking and not boosting. Please correct me where I am wrong.
In Boosting methods,  the based classifiers are the same. But the given in Matlab code for AdaBoost combines different classifiers, I am not sure.

2) Is ensemble learning or the example in the ensemble toolbox the same as the Adaptive Boosting Matlab code (second link)? Is ensemble learning the same as Adaptive boost?
Ensemble learning combines predictions from multiple learners. Boosting methods are one way to form an ensemble. Stacking is another. The important difference between boosting and stacking (and other ensemble methods) is that boosting applies a number of weak learners sequentially and then produces a final result via a weighted majority vote.

The learners in stacking can also be combined as a weighted average or vote (or by another "meta" model) but they can be more or less independent. 

In boosting, each weak learner (usually the same, yes) modifies the data for the next learner in the sequence. E.g. in AdaBoost the weight of each learner and also each sample in the data depends on the misclassification rate of the previous weak learner to the effect that the next learner focuses more on previously misclassified samples. 

Boosting methods typically vary by how these weight updates are performed.