Elie Tahari is the "designer" version, with higher prices. Tahari is a lower-priced version from the same brand, and Tahari Arthur Levine is a collaboration line.
Many designers do similar things. For example, a Marc Jacobs bag is significantly more expensive than a Marc by Marc Jacobs bag. Kors and Michael by Michael Kors are less expensive versions of the Michael Kors line.
In most cases, there is definitely a difference in quality and construction. For example, there is no comparison between a Skorpios bag by Michael Kors and Hamilton bag from the Michael by Michael Kors line. Both are nice bags, but holding both, you would never confuse the Hamilton for the higher-priced version.
While Coach hasn't actually changed the name, their Poppy line is something similar and is intended to be lower priced and to attract a deifferent demographic.