I know that they are two different genes, but they both dilute black. Lavender also dilutes buff. Blue (Bl) dilutes black to blue when heterozygous and splash when homozygous. This dilution is not even, though. Blue chickens will have lacing and darker parts. Splash birds will be "splotchy". Lavender (Lav) only expresses itself when homozygous, and it dilutes to a very even color.
Blue and splash birds can also carry lavender if it's bred into them. I understand that a homozygous lavender bird with one or two blue genes will not look the same as a lavender bird without a blue gene. Someone else will have to educate you on that, as I have no experience with it. I DO see birds on eggbid that are advertised as lavender splash, and they just look splash.
I don't have any pics of blue or splash, but here are two lavender Cochin brothers, Sterling and Captain McCrae:
In addition to what has been said, andalusian blue, commonly called blue, on top of being dark blue grey in color, doesnt breed true in 100% of cases either. Lavender, commonly called, self blue, does breed true, and is that very pale powdery blue pictured above.
Both can be used to replace black on birds, however, the lavender will also lighten the majority of other colors too. In addition, any bird bred to a. blues, will eventually produce blue, black, and a sport/splash pattern in the color bred to. Usually at a ratio of 50% blue'and 25% each for black and sport.