The weapon types indicate which research upgrades affect them.  TEC have autocannon, laser, missile, and beam (entrenchment only) upgrades.  Vasari have pulse, wave, pulse-beam, and phase missile upgrades.  Advent has laser, plasma, and bream upgrades.  In general most players will focus on one or two types of upgrade.  This varies for each faction and unit type. 

Aside from this, there's also damage types as described by Arthanis.  All heavy cruisers (regardless of faction) have composite damage and very heavy armor, meaning they counter units with light armor (long range frigates) and are countered by units with anti very heavy damage (bombers).