I have studied algorithms for clustering data (unsupervised learning): EM, and k-means. 
I keep reading the following : 


  k-means is a variant of EM, with the assumptions that clusters are
  spherical.


Can somebody explain the above sentence? I do not understand what spherical means, and how kmeans and EM are related, since one does probabilistic assignment and the other does it in a deterministic way. 

Also, in which situation is it better to use k-means clustering? or use EM clustering? 

K means 


Hard assign a data point to one particular cluster on convergence.
It makes use of the L2 norm when optimizing (Min {Theta} L2 norm point and its centroid coordinates).


EM


Soft assigns a point to clusters (so it give a probability of any point belonging to any centroid).
It doesn't depend on the L2 norm, but is based on the Expectation, i.e., the probability of the point belonging to a particular cluster. This makes K-means biased towards spherical clusters.

