[python] In TensorFlow, what is the difference between Session.run() and Tensor.eval()?

Tensorflow 2.x Compatible Answer: Converting mrry's code to Tensorflow 2.x (>= 2.0) for the benefit of the community.

!pip install tensorflow==2.1
import tensorflow as tf

tf.compat.v1.disable_eager_execution()    

t = tf.constant(42.0)
sess = tf.compat.v1.Session()
with sess.as_default():   # or `with sess:` to close on exit
    assert sess is tf.compat.v1.get_default_session()
    assert t.eval() == sess.run(t)

#The most important difference is that you can use sess.run() to fetch the values of many tensors in the same step:

t = tf.constant(42.0)
u = tf.constant(37.0)
tu = tf.multiply(t, u)
ut = tf.multiply(u, t)
with sess.as_default():
   tu.eval()  # runs one step
   ut.eval()  # runs one step
   sess.run([tu, ut])  # evaluates both tensors in a single step