In Georgia, we have split-levels.
I live in a split-level. You walk up 15 or so steps to get to the front door, walk in and you are on a small landing basically (called foyer though). You can go down 8 steps to the den, BR#4, Bath and laundry room. From there you can go out to the patio (down about 4-5 steps) or out to the garage (down about 4-5 steps). Back to the front door, you can go up 8 steps to the main level and rest of the house. Living room, dining room, kitchen, master bed/bath, 2 other bed and one other bath. The land is pretty flat where the house actually is.
My parents live in a tri-level. You walk up 8-9 steps to get to the front door. Go in and you have an entry way and living room. That level also has the family room, kitchen and dining room area (really part of the living room). There's also a screened in porch in the back on this level (no steps). In the "center" of the house are two staircases. One going up to the 3 BR and 2 BA and one going down (with a door) to the garage (which my Dad turned into an office and storage so it's now more like a basement). The laundry is down there too.
My house only has two levels of living. My parents have three.
I never realized or thought about that a certain style name could mean something different elsewhere in the country. If we ever move out of GA, I'll have to do my homework!