You can get different strains.
The second time possibly was a virus that wasn’t “influenza” per se, but it could have been a different strain thereof.
The chances are getting two are possible but not usual. Otherwise, doctors would be sick all the time. The dr in my Bible Study was vaccinated and still got the flu but he was inundated with sick patients. Law of averages catches up to you after a while.
BTW I got the flu vaccine one year and still got the flu. But a dose of Tamiflu and I was fine in a couple of days. The people I knew who rode it out had problems for months.
Note; In the Spring of 1918, the Spanish Flu appeared but it wasn’t fatal and died off when flu season ended. When the Fall flu season began, it wiped out entire villages.