Two ‘Social Security Numbers’?

Also in January I received a letter saying;

Suite a la declaration de votre activité en tant qu’auto-entrepreneur, j’ai le plaisir de vous informer que vous êtes affilée a la Sécurité sociale pour votre protection social obligatoire a compte du 27/12/2020.

It also gave me a social security number (à rappeler dans toute mes correspondance) which I was pleased about, but when I used that to choose my Dr, they said they couldn’t find that social security number in their fichier.  The number has five zeros in the middle.  I then received a further letter, a Declaration du Chiffre d’affaires Trimestre 4e 2020, with the social security (SS) number provided differing in last two digits.  I thought this just signified the permanent rather than the provisional SS number, but when I phoned CPAM directly they said the URSSAF SS number is not the same as the Ameil/CPAM SS number, even though they’re both described as the social security number.  She said they have wrangled over this for years because they know people get confused.  So, my understanding now is that the two branches of gov - Work/Pensions & Health - that use the same descriptor ‘Social Security number’ but they are not interchangeable - is this right? 

Can you explain the discrepancy between the two URSSAF numbers ?

And whether it is true that both the Health and URSAFF give people ‘social security numbers’ but which just apply to either their health provision or their tax work/pensions rights?