What is the difference between principal component analysis and factor analysis?

What's the difference between MDS and PCA?

• How are they similar? How are they different? When would I use one over the other? Under what circumstances do they produce different results? A practical (intuitive?) answer is the most useful one.  I'm quite comfortable with PCA, can do the math; and I also get most of factor analysis.  And I know MDS uses a distance matrix, whereas PCA uses a correlation (or variance-covariance) matrix. My intuitive understanding is PCA is like taking a snapshot of a cloud of data points from each dimension (eigenvector), whereas in MDS you pound that ball into an n-dimensional pancake (where you define n).  Does that analogy work? I am aware of http://stats.stackexchange.com/questions/14002/whats-the-difference-between-principal-components-analysis-and-multidimensional but find it insufficient, and would like to see what Quora can give me.

• Answer:

  PCA minimizes dimensions, preserving covariance of data. MDS minimizes dimensions, preserving distance between data points. They are same, if covariance in data = euclidean distance between data points in high dimension. They are different, if distance measure is different.