Simple Difference would be:
Design Patterns:
Solutions which are productive and efficient and are developed by Software Engineers over the years of practice and solving problems.
Anti Patterns:
Known solutions which are actually bad or defective to certain kind of problems.
From Wikipedia:
An anti-pattern is a common response to a recurring problem that is
usually ineffective and risks being highly counterproductive.[1][2]
The term, coined in 1995 by Andrew Koenig,[3] was inspired by a book,
Design Patterns, which highlights a number of design patterns in
software development that its authors considered to be highly reliable
and effective.
The term was popularized three years later by the book AntiPatterns,
which extended its use beyond the field of software design to refer
informally to any commonly reinvented but bad solution to a problem.
Examples include analysis paralysis, cargo cult programming, death
march, groupthink and vendor lock-in.
Example of some anti patterns:
- https://javaantipatterns.wordpress.com/
- https://sourcemaking.com/antipatterns
Hope this makes sense.