Sabino, Frame, & Splash are all grouped together as "Overo" patterns. Frame Overo is the gene that people are talking about when they say "Lethal White", because it is fatal when homozygous. It's also responsible for the patterns that most people think of when they picture an Overo horse. It's called "Frame" because it literally looks like the colour is framing the white. Frame is a pattern gene that manipulates other pattern genes. When it's by itself, or when the other pattern gene is very minimally expressed, the horse can look almost solid, like yours. However, when the other pattern gene has more expression, it tends to look something like this:
Frame + Sabino
Frame + Sabino
Frame + Splash & maybe Sabino
You could still call her a Bay Overo. Registration-wise, she'd probably be considered solid-coloured since she has so little white.
Yep. Tobiano goes over the back. The various types of Overo do not, with the exception of very extreme cases (Maximum Sabinos can appear all white).
Splash White is called so because it basically looks like the horse has been dipped feet first into a can of white paint. They characteristically have high white socks, white extending up from their belly, & bald white faces that very frequently include white over their eyes. Minimally expressed Splash horses typically have a crooked stripe down their face or a snip. The gene can cause blue eyes. Their tails tend to go white from the bottom up (which is opposite from a tobiano). The so-called "medicine hat" paints are generally horses who are thought to be homozygous for Splash who are also carrying Tobiano. When Splash & Sabino are together, it tends to cause black eyeliner. There is currently no genetic test for Splash.
Splash & Sabino (note the eyeliner):
Sabino can look quite similar to Splash sometimes, however there are differences. Sabino does not cause blue eyes. They do not necessarily have all white legs, although it is a very common feature. Their back legs will often have tall, jagged stockings that reach all the way up to their belly. Their markings are not as cleanly expressed as Splash is, & tend to look messier around the edges. The white on their faces avoids their eyes, and they often have dark mustaches. Sabino can cause extensive "roaning" (although not true roan) throughout a horse's coat, which generally starts from the belly up. Many horses with very tall stockings and big white blazes are actually Sabino. Currently, the only type of Sabino that can be tested for is called Sabino1. It is speculated that some form of Sabino is responsible for all white markings, although no one has developed a test to prove this theory yet.
Sabino with heavy "roaning":
Usually when I think of "crossing the back", I think of the actual back like in the 5th & 8th pictures, not the tailhead. Although I would consider most of those horses to be pretty extreme Splash! Horses #5, #8, & #9 are Splash + Sabino
That black filly on the bottom is definitely Splash as well, look at her tail. If she was just Tobi, it wouldn't be white from the bottom up like that. I looked up her sire, I'm guessing he was probably Tobi, Splash, & Sabino.