Universal design tries to plan and manufacture products (environments, buildings, furniture, etc.) that can be used by everybody, regardless of their age, gender or possible disabilities. Usually UD is used in context of physical objects, not software.
User-centered design is a user interface design method that focuses the needs, goals and limitations of end users - in contrast of e.g. a features-first designed UI.
Albeit, if we extend the methods to software, they are not exactly the same, but share some characteristicts. I'd say that UD is a subset of UCD. Usually, a big part of UCD is the participation of the actual users (in form of either cooperative, participatory or contextual design), not necessarily a part of UD.
"Universal design" or "Design for all" is a design metodology focused on inclusion of all user, expecially users that has different mobility o perception. UD aims to make barrier-free products.
UCD instead is a design metodology where the user behavior and their characteristics are pointed as the main factors.
UD is UCD, but UCD is not always UD.