Oh yes.  You can have both on the same bird.   Breeders who are dealing this mess call the blues Andalusian Blues and the Splashes Andalusian Splash.  Lavender is another term for Self Blue. 

A Silkie that is lav/lav (Homozygous Self Blue) and Bl/Bl (Splash) can be called Self Blue Splash.

I've been dealing with these colors for about two or three years now. What I'm getting ready to describe is not based on detailed research but are my impressions - which are shared by several other breeders dealing with the same genetic base. 

Self Blue Splash

On males Self Blue Splash is an odd splotchy color that is neither Self Blue nor Splash.  You'll have a nice shade of light blue as the background color and a few dark blue feathers at irregular intervals on the coat.  The Self Blue Splash females are a little prettier.  They are less irregular looking than the Andalusian Splash females and almost look speckled.  Again, on the Self Blue Splash females, the background color is light blue with darker spots. 

Andalusian Splash

With Andalusian Splash males and females, the background color is near white with black and very dark blue feathers at irregular intervals in the coat.

Self Blue

A Self Blue male and female should be an even shade of light blue all over. 
 

It is a long story but I believe that most show quality Blue flocks in the United States and many show quality Black flocks now carry the Self Blue gene.  I actually own a small handful of Splashes that I am almost certain do not carry Self Blue.  They are old birds and I hope to increase their numbers this year.

©2007 American Silkie Bantam Club