Bagging trains many models independently, each on its own bootstrap sample, and combines them with an equal-weight average or vote. Boosting trains models one after another, each focusing on the examples the ensemble still gets wrong, and combines them in a weighted sum. Bagging mainly reduces variance; boosting mainly reduces bias.
AdaBoost shows the sequential part. Give 10 training points weight 0.1 each. The first stump misclassifies 3, a weighted error ε = 0.3, so its vote is α = ½ ln((1 − ε)/ε) ≈ 0.42. Misclassified weights are multiplied by exp(0.42) ≈ 1.53, the rest by exp(−0.42) ≈ 0.65; after renormalizing, the 3 hard points hold 50% of the weight, up from 30%.
This decides the base learner. Bagging needs strong, unstable models such as deep trees, since averaging cannot remove errors every model shares; weak learners such as stumps belong to boosting. Bagging runs in parallel and adding models does not overfit; boosting is sequential, needs a learning rate and early stopping, and can chase mislabeled points.