There can be inequivalent Legendrian knots that are isotopic as topological knots. Many inequivalent Legendrian knots can be distinguished by considering their Thurston-Bennequin invariants and rotation number, which are together known as the "classical invariants" of Legendrian knots.
The distinction between inequivalent Legendrian knots is based on their topological properties, specifically their Thurston-Bennequin invariants and rotation numbers, which are collectively referred to as the "classical invariants" for Legendrian knots.