The image on the mod doesn't affect the stats on the mod itself. All mod sets roll from the same pool of stats.
When you equip enough mods from the same set, you'll get a bonus based on the set. In the example you provided, you should have gotten a Defense set bonus. This doesn't show up on the mods themselves, it just gets added to your character's stats. You can see which bonuses are active by looking at the circles below your equipped mods, as indicated by Kyno above.
Offense, Crit Damage, and Speed sets require four mods, so you can only get one of those set bonuses. The other sets only require two, so you could get each of those set bonuses as many as 3 times.
The bonus is calculated off your character's "base stats," which I believe means any stats they have unmodded and not counting any gear they haven't yet "absorbed" i.e. if your character is at gear 11 and has one of the +6 speed detonators equipped towards gear 12, a speed set won't count that 6 speed when calculating how much the set bonus adds.