They both reflect responsibility. If you're going to criticize people for giving Trump credit for being responsible to direct the Navy to do stuff (that's his call to make), you should not blame Obama for directing his staff and his sycophants in the Congress to write legislation. Bottom line, the president gets blame and responsibility for what happens when he's president, despite having no direct involvement.
In the case of ObamaCare, Obama was an active participant in the process. It was his idea, he worked with those in congress to get it passed and even used his political capital to make it happen. He did not just sign it, he was not an inactive bystander in the process.
In the case of Trump ordering a ship to go somewhere, that is where his involvement ends. He is not involved in the process or any of the work to make it happen.
Huge difference between the two.
In our society today, what blame or credit someone gets is based solely upon the party of the person assigning each. I try very hard to do it equally to both sides.