Halo 5 has two main teams in the story line; Blue Team and Fire Team Osiris. Is there a difference between a fire team and a non-fire team?
Master Chief and his team are Spartan-IIs. The Spartan-II program was split into 5 teams Blue, Grey, Green, Red and Black.
Locke's Team are Spartan-IVs. The Spartan-IV program was split into 23 teams. The name of all of these teams follow the format of 'Fireteam X'.
Wikipedia defines a fire team as "...a small military sub-subunit of infantry designed to optimize bounding overwatch and fire and movement tactical doctrine within a hostile urban environment."
While both teams can be classified as a Fireteam in the military sense, the only reason for the name difference in the game is the naming conventions for the different spartan programs.
Fire team : Team of Locke the evil bastard (I hope he dies painfully)
non-Fire team aka Blue Team: Teach of Master Chief Spartan 117. Savior of humanity of the galaxy, demon the covenant.
They both have different missions, fire teams is like the dog that runs after the car (in this case blue team)
Blue team's mission is to save Humanity from the upcoming threat.
They have different squad meembers and thus different 'power ups' and play style. you've to play with your friends to experience it.