One difference: the seasonal flu vaccine is based on predicting ahead of time which strains of flu are likely to circulate during the upcoming flu season and targeting those strains. Sometimes the predictions are accurate, sometimes they’re not. The H1N1 vaccine targets a specific strain that we know is circulating.
In RFC terms:
A seasonal flu vaccine MAY protect you from seasonal flu.
An H1N1 flu vaccine SHOULD protect you from H1N1 flu.