It's not clear which specific 'Caine' is being referred to here. It could be the character from 'Kung Fu' or some sort of made - up or less - known reference to a character in the world of 'Pulp Fiction' that has some connection to the idea of 'Caine' from 'Kung Fu'.
Overall, Trigun Stampede adheres closely to the manga. Some minor details might differ for the sake of the adaptation's flow and visual presentation, but the core remains the same.
The Trigun manga has a considerable length. It consists of multiple volumes and chapters, but the exact number can vary depending on the specific edition and printing.
One characteristic is that it often contains romantic or more sensual elements related to the characters of Trigun. It may focus on relationships between characters like Vash and other main characters in a more intimate way.