If I am out of range 1 of an enemy squad and command my squad to move then shoot an enemy SHIP but end my movement within 1 of the enemy SQUAD am I now engaged and must shoot squad instead?

Yes. As soon as you're within 1 of an enemy (non-heavy) squadron you're engaged.

Worth remembering that the ship itself will block line of sight, so two opposed squadrons on opposite sides of a ship are not engaged with each other even if within distance 1.