ADA’s regulations specifically state only service animals which are dogs are considered to be under the act, and they must perform a service. They are required to be under the owner's control at all times when outside of the residence.
HUD’s service animals don't operate under the same restrictions and are oriented towards residences.
All service animals under all regulations require training (can be trained by the owner), none require certification (except for a non-apparent disability where a request can be made for confirmation of the disability such as a doctor's note.)
There is a movement to amend HUD’s regulations to require therapeutic goals for ESAs and amendments to ADA to include specific waivers for additional animals (which might even take out the self training and require actual certification.)
Truthfully, this would have been done years ago, but the rampant abuse of the service animal laws, as you point out, is creating quite a lot of resistance to any fixes - both by the abusers and those who want to put an end to the abuse.
Honestly, I'm sure it will likely drift for another couple years until 2020 when HUD goes through their review process again and likely tightens quite a few regulations. Likely any modifications for ADA will come from state level actions first.