Confused about the different aspects in Machine Learning
Good question and welcome to Datascience

Imagine you have the tree as follows.

                 Machine Learning Models
                          |
           ----------------------------------------------------
           |                                                  |
       Supervised                                         Unsupervised
           |                                                  |
   - --------------------                                  Clustering
   |                    |
Regression          Classification


A model is indeed a trained version of the algorithm you are chosing,
regardless of whether its Regression, Classification or Clustering. The above
tree is ofcourse a simplified version of all ML algorithms.