The game is sometimes confusing about the difference between skill points, skill levels, and skill values... I don't even know what the proper names for them are.
If you put 200 skill points into, let's say, Combat Maneuvers, to bring it to level 1, you actually gain +8 to your Combat Manevuers skill as seen in the character passives or detail window on the skill tree. When you see skill bonuses on equipment or traits, that last one is what's actually increasing.
Joined Trill is comparable with an Alien character which has the Efficient Trait. They're almost identical and buff your powerlevels. The Efficient Trait only buffs your space power levels if you keep them at 75 or below. For me it's still better to have an alien than Joined Trill because most of the time i run my powers 100/25/50/25. (But that is just my personal opinion.)
So exactly how does "bonuses to training" reflect in terms of weapon/shield/engine/ability effectiveness?
Skill bonus is the value that shows above each rank bar in the powers window from the Skills Window. For a T1 skill that would be Rank 1, == +6, Rank 2 == +10, ...Rank 9 == +18. The skills bonuses are percentages which add to the character abilities. And from the zen of power there are 3 Captain skills which modify them. All 3 skills are Rank 9 gives a Skills Bonus os +100%.
The Joined Trill skills bonuses are added to the skill bonus gained from Captain Skill ranks. The skills bonuses may seem small. But all of the Joined Trill bonuses are Basic skills so they affect a bunch of Captain and BO abilities.