You ask a good question that has many different answers depending on who you might work for, and who their client is, where the job is located, what type of job it is, and what they mean by the term “rigger.”
An API “rigger” is just a guy who has had a 4 hour or 8 hour “rigging” class that merely prepares him to connect crane hooks to pre-slung loads in the oil patch. Frankly, the API “rigging” class is pathetic.
Some oil patch companies require that you a tend a specific course at a specific school that is 1, 2 or 3 days long.
An NCCCO “rigger” is trained to actually rig loads and give crane signals, not merely make hook connections. NCCCO meets OSHA standards for riggers. It’s the gold standard in the US.
An NCCER “rigger” is also OSHA compliant is what many construction companies and some unions prefer.
There are other competing rigger schools and certification standards in the US which also meet OSHA requirements.
No matter what rigging training you obtain, some employers, unions, or clients, may expect you to get additional training that specifically meets, and provides a pocket card and certificate for, whatever rigging standard they have adopted.
The API “rigger” class is fast, easy, and cheap.
I once had a non-oil patch employer who said that my API “rigger” card was “close enough,” instead of the NCCCO card that the job posting called for.