critical current is the maximum electric current a superconductor can carry before superconductivity breaks down and electrical resistance returns.
Written I_c, the limit is not fixed the way a material's 📝critical temperature is: it depends on how cold the conductor runs and how strong a magnetic field it sits in. A 📝superconductor operated far below its critical temperature and in a weak field carries far more current than the same conductor near either limit, so critical current is best pictured as a surface over temperature and field, and a magnet's operating point must stay under it everywhere. Engineers also distinguish the critical current of the superconducting layer itself from the engineering current density of a practical conductor, which averages the current over the whole cross-section — substrate, cladding, and all.
The near-neighbor to keep distinct is the 📝quench: critical current is the boundary, while a quench is what happens when the boundary is crossed and the conductor's stored magnetic energy suddenly converts to heat in a resistive spot. Fusion magnet design lives inside the critical-current surface with deliberate margin — the coils of 📝High-Temperature Superconducting (HTS) Magnets carry tens of thousands of amperes precisely because REBCO retains a usable critical current at fields around 20 tesla, where earlier superconductors carry essentially none.