3-Tab asphalt shingles have three regularly spaced tabs, giving the roofing material a very repetitive pattern and flat appearance. They carry a 25 year manufacturers warranty and are the most cost effective.
Dimensional also known as Architectural shingles have two layers of shingle material bonded together, giving them a three dimensional wood shake appearance. They carry a 30yr/lifetime manufacturers warranty depending on the brand.
Regular dimensional shingles have some color variations and have some dimension to them but tend to keep the colors more blended. This style works well on homes that have bold brick or siding while the Maxdef and HDZ work well on homes with more muted brick or siding.
Maxdef or HDZ shingles have more color variations to them making a more dramatic appearance. Some brands will use the same colors just different shades to cause the dramatic effect, while other brands like to add more colors to make the shingles pop. These look great on homes with less bold brink or siding.