the radical is just the symbol √ and the surd is the actual expression for the number, which often uses radicals.
For instance, √7 would be a surd, since it is a well-formed expression referencing the positive root of x^2 - 7; meanwhile, √ is not an expression, so it isn't a surd.
Surds are unresolved radicals, such as
square root of 2
cube root of 5
These are examples of surds that are irrational numbers, since they cannot be expressed as ratios of integers.