If the tempdb is full, all databases in the instance stop accepting updates. Error code will be 1101 or 1105.
If the transation log if full, error code is 9002. Only the database stop accepting updates.
SQL Server severity is from 0 to 29. The higher the severity number, the more severe the problem. By default, only error messages with a severity level above 19 are written to the SQL Server error log.