Typically what I've seen on jp, and it might be different on EN, is:

There is the generic premium gacha which gives you whatever chance of 3*, 4*, 5*, 6* ... and then every 3* has the same chance as every other 3*, every 4* has the same chance as every other 4*, etc. [B]As more girls are added in each rarity, it will be harder to get specific girls from that rarity. If you really want Toad Lily, for instance, NOW is the time to go after her[./B]

There is also a spotlight premium gacha whenever they add new non-event 5* and 6* girls. Typically they add two 5* and one 6*. The only difference between premium and spotlight is that, if you get a 5*, you're more likely to get a 5* in the spotlight. It won't change the rate of giving 5* or 6* units in general, so if you DON'T like the current 5* or 6* units, you can save up flower coins for future spotlights.

I've also seen bonus gachas that add manyu or evolution units in addition to the flower knights, or spotlights that actually target a type of unit (blue/purple/yellow/red).

Finally, there have been step up gachas and other special offers that used dmm gold directly and had their own methods of working, but... well... Nutaku will do its own thing there I'm sure. Don't rely on them copying dmm's offers.

My advice on using premium gacha: When you hit 50 flower coins, do the 11-spin gacha once for some stronger units to build your team around. Then save up coins so you can do the 11-spin several times when you really, REALLY want two or more of a set of spotlight girls.