The three modes
Arcade Battles (AB) use simplified physics, lead indicators and respawns, and matchmaking based on an averaged Battle Rating of your top vehicles. It is the accessible entry point.
Realistic Battles (RB) are where most of the playerbase lives: realistic flight and ballistics, limited markers, and matchmaking based on the highest Battle Rating in your lineup. Expect one life per vehicle in air RB and lineup respawns in ground RB.
Simulator Battles (SB) are the most demanding: cockpit and instrument views, no markers and full realism. Ground SB uses an allowed-vehicles list rather than a pure BR range.
Battle Rating (BR)
Every vehicle has a Battle Rating, a balancing number independent of its research rank or your skill. The scale runs from 1.0 up to roughly 14.7 at the very top tier (air), and the matchmaker forms battles of lineups within about ±1.0 BR of one another.
The practical takeaway: your lineup's BR — not any single vehicle — determines the enemies you face. Keep vehicles of similar BR together, and be wary of "uptiers" where you are matched against opponents up to a full BR above you.