word choice - Difference between "evade X" and "sidestep X"?

Please consider the following sentences

In the journalist meeting, the politician evaded the questions about riots.
in the journalist meeting, the politician sidestepped the questions about riots.

Do those sentences have the same meaning?

As fundamental rule, no two words would have same meaning at all times. I expect some differences between evade and sidestep, which is why I am asking this question.

The "Dictionary" software which I am using shows these definitions:

Evade = escape or avoid, esp. by cleverness or trickery
Sidestep = avoid (someone or something) by stepping sideways

I am unable to make out the differences between those two definitions.