For Heliolisk/Pyroar, they're saying only part of them (solar energy frills/fire mane) are elemental. The rest of their body is non-elemental.
For Girafarig/Sawsbuck, there's a dual-being theme going on.
For Bibarel/Diggersby, I guess they're saying they became better at swimming/digging but didn't really gain magic powers over their element and still tend to hang out on the land.
For Wigglytuff/Exploud/Meloetta, there's the obvious sound connection.
Chansey is likely because of balancing reasons.
Not sure about Audino. I think they just fucked up there.
I've heard theories that Azurill had some of its stats copypasta'd from Cleffa or Igglybuff, hence the gender ratio and type disrepancy.
Everything else is either a (relatively) non-descript mammal/bird/reptile, type changer, or retconned Fairy.
