PUD in real estate stands for Planned Unit Development. A Planned Unit Development is a community of single family homes that belong to a homeowners association or "HOA".
You can think of the PUD as the physical development (community), and the HOA as the governing body of the PUD. So let's say you have a community of 100 townhomes in a 5 acre tract of land. That is the PUD -- true to its name it is a planned development. The HOA is the association of property owners which is overseen and managed by a board of directors or a 3rd party management firm. The HOA is typically a corporation in legal structure that enforces bylaws, votes on new laws, manages community events and collects annual dues. Many HOAs have committees such as landscaping committee and architecture committee. HOAs tend to be governed by a board of directors with roles such as president, treasurer, safety liaison, etc.
A planned unit development or PUD is a residential real estate development that is typically built by a common developer and intended to be a uniform community governed by a homeowners' association or HOA.
PUD is the physical community of homes typically build by the same real estate developer, and the HOA is the organization that manages the community on an ongoing basis.