This time was different.

When Craig Spencer, a young doctor just back from treating patients with Ebola in Guinea, fell ill with the virus in New York on Thursday, the paramedics who went to get him were dressed in protective suits. He entered Bellevue Hospital through a rear door, far from the busy emergency room, and was taken to a state-of-the-art isolation ward that was locked and guarded.

The carefully planned response was a world apart from the scene that unfolded in a Dallas hospital last month when a Liberian man, Thomas Eric Duncan, became the first person to test positive for Ebola in the United States.

It was Ebola’s first surprise encounter with a modern medical system, and it was, by all accounts, a bumpy one. Mr. Duncan lay in an emergency department room at Texas Health Presbyterian Hospital for hours, with a fever and frequent diarrhea, while the same doctor and nurses treated patients in nearby rooms, medical workers said. A lab technician had to comb through his inbox to find an email from the government on procedures for Ebola blood samples, only to find that he had handled them improperly, the workers said.

Rules for protective gear seemed to change with the weather, and some of Mr. Duncan’s nurses, unsure of what to wear, resorted to looking for answers on the website of the Centers for Disease Control and Prevention, according to a health worker involved in the response.