Ah glad I didn't bombard you with useless information then!
Here is some more information. I wouldn't blame you for skipping it though as it's kind of a lot for someone new to chickens!
It looks like your little showgirl Snuggles and the frizzled grey both have silkied feathers and would be considered silkies.
The rest all look like they have non silkied feathers so would be considered satins (yours all look like smooth satins).
Both silkies and satins can come in the frizzled variety. It's harder to tell with frizzled silkies though as they often just look a bit more fuzzy/frizzy than non frizzled silkies. I'm pretty sure your little grey frizzle is indeed getting frizzled silkie feathers.
It's likely that the breeder just didn't know regarding the satin vs silkie thing or doesn't consider them different breeds. Things surrounding satins have changed a lot and it can be hard to keep track of at times. At first those working on satins as a project breed did try to get them recognized as a type of silkie but that didn't work out (that was back when they were called sizzles rather than satins). Now they consider them an entirely different breed but still breed to the same standard other than the non silkied feathers. Satins still aren't a recognized breed though and are considered a project breed.
The regular non silkie feathering is dominant so even if a silkie has satin ancestors it'll never produce a satin when paired with another silkie (barring some weird genetic anomaly). Since silkie feathering is recessive you can breed two satins together and still get a silkie if they both carry a copy of the recessive silkie feathering gene though.
This dynamic makes satin/silkie pens a lot of fun since you can get such a variety of feather types.
Paint and splash are definitely similar but different genetically. Splash is made with blue genetics (two copies of blue makes splash) and paint is made with dominant white over black. Generally paint has a more white background with black spots while splash has a very light blue/gray background with varying shades of blue streaks/spots.
Visual examples always help me more though so maybe these will be useful.
Paint silkie chick
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Paint silkie
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Splash silkie chick
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Splash silkie
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