DMAIC stands for Define-Measure-Analyze-Improve-Control
Basically this is for existing enterprises and comprises of the following steps:

• Define high-level project goals and the current process.  
• Measure key aspects of the current process and collect relevant data.
• Analyze the data to verify cause-and-effect relationships. Determine what the relationships are, and attempt to ensure that all factors have been considered.  
• Improve or optimize the process based upon data analysis using techniques like Design of experiments.
• Control to ensure that any deviations from target are corrected before they result in defects. Set up pilot runs to establish process capability, move on to production, set up control mechanisms and continuously monitor the process.

DMADV stands for Define-Measure-Analyze-Design-Verify

This methodology is for a proposed new start-up enterprise/venture and consists of the following five steps:
Define design goals that are consistent with customer demands and the enterprise strategy.

• Measure and identify CTQs (characteristics that are Critical To Quality), product capabilities, production process capability, and risks.
• Analyze to develop and design alternatives, create a high-level design and evaluate design capability to select the best design.
• Design details, optimize the design, and plan for design verification. This phase may require simulations.
• Verify the design, set up pilot runs, implement the production process and hand it over to the process owners.