If it's just a coaching, not all leaders will say it's documented. Document coaching is pretty much them just telling HR they spoke to you about something. Therefore, they don't always say it's a write up.
CAs they definitely should say it's being documented, as that's a write up. Then you'll be spoken to again and presented with the write up, and you'll have the option to sign or not. Now if it's compliance, you'll have to sign a booklet and an ETL will just tell you to be mindful of your breaks. As stated above, in Cali it's more serious.