The differences between Articles 358 and 359 can be summarised as follows:
Article 358 is confined to Fundamental Rights under Article 19 only whereas Article 359 extends to all those Fundamental Rights whose enforcement is suspended by the Presidential Order.
Article 358 automatically suspends the fundamental rights under Article 19 as soon as the emergency is declared. On the other hand, Article 359 does not automatically suspend any Fundamental Right. It only empowers the president to suspend the enforcement of the specified Fundamental Rights.
Article 358 operates only in case of External Emergency (that is, when the emergency is declared on the grounds of war or external aggression) and not in the case of Internal Emergency (ie, when the Emergency is declared on the ground of armed rebellion). Article 359, on the other hand, operates in case of both External Emergency as well as Internal Emergency.
Article 358 suspends Fundamental Rights under Article 19 for the entire duration of Emergency while Article 359 suspends the enforcement of Fundamental Rights for a period specified by the president which may either be the entire duration of Emergency or a shorter period.
Article 358 extends to the entire country whereas Article 359 may extend to the entire country or a part of it.
Article 358 suspends Article 19 completely while Article 359 does not empower the suspension of the enforcement of Articles 20 and 21.
Article 358 enables the State to make any law or take any executive action inconsistent with Fundamental Rights under Article 19 while Article 359 enables the State to make any law or take any executive action inconsistent with those Fundamental Rights whose enforcement is suspended by the Presidential Order.
There is also a similarity between Article 358 and Article 359. Both provide immunity from challenge to only those laws which are related with the Emergency and not other laws. Also, the executive action taken only under such a law is protected by both.