Even though all weapons only have 1 active skill, different weapons have varying unique abilities. Some have unique playstyles like having charge attacks or special moves when they are charged in the middle of the combo. There are also aerial attacks, different dodge skills, as well as passives to consider, so it's always recommended to at least glance at what they can do to bring out their full potential.
You can view a weapon's movesets and their multipliers by selecting on the "!" button below the weapon's icon image when viewing a weapon.
Resonance
Weapon resonance is a form of passive buff that you can get if you bring 2 weapons that have the same weapon type (DPS, Defense, Support) into battle. The resonance effects can be quite impactful, but won't be that noticeable since it works like a passive.
If all the weapons that you bring are all different types, you will only get a 5% damage bonus from the "Dissonance" effect, compared to 10% from getting the "Attack" effect.
Using 2 defensive types will give some damage reduction, but also increases enemy aggro. Using 2 support type weapons will increase healing.
Most of these effects are increased even further in team play, which makes it even more important that you focus on one of them instead of using Dissonance.
Relics are like equipable items that can be used to help with exploration or fights. Jetpack and Jetboard make exploration easier and you get them automatically by progressing through the story, while Relics like Missile Barrage or Strange Cube are obtainable by doing "Ruins".
Since you can only bring 2 at a time, you can equip 1 for exploration and the other for battle.
It may not deal a lot, but it helps deal additional damage when you're fighting, especially since Relics are like skills since they're free to use and is only limited with a cooldown.
Relics can be powered up by using their own Relic shards to advance them, which you can get by doing their respective Ruin dungeon.