There's a lot more to engine oil than viscosity and synthetic* - the ACEA category is important to avoid contaminating the emission controls on modern engines, ie anything after about 1990 - the car manufacturers' approval reference is vital.
* except in Germany, "synthetic" oil isn't actually synthetic - it's hydro-cracked mineral oil in the rest of the world - "synthetic" is just a marketing term that doesn't form part of any oil specification.
You’re right, there’s more to it than viscosity grade and claimed base oil type. There’s also more to it than ACEA specification too - many OEMs publish their own oil specifications, which go beyond the general requirements of ACEA or API and include OEM-specific demands. It is best to check the user manual for what oil specification is required and then find an oil which is approved to that spec.
The “synthetic “ thing is a bit more complex than you state. A synthetic oil can be made with a number of different base oil types:
- PAO, known as “group IV” - these base oils are synthesised from gas molecules. These are marketed as “synthetic” globally
- hydrocracked, known as “group III” - these base oils are synthesised from a waxy refinery output; what you end up with is totally different from what you started with, hence “synthetic”. These are marketed as synthetic globally - in Germany they are specifically called out as “HC-synthese”.
- esters, part of a broad group of base oils known as “group V”. These are petrochemicals that are expensive and so only used in fairly specialised products.
There are a few other base oils that can be synthetic but are rare and specialised.
Any given engine oil is made using are least two base oils, in order to get the final viscosity right. These base oils can be of the same type or from different groups. If they are a mix of groups III, IV and certain Vs then the product is called fully-synthetic. If they mix a group III with, say, group II or I (both are highly-refined mineral oils) then terms like semi-synthetic, part-synthetic etc are often used.
However, none of these terms are really important to the end user. What is important is what performance specifications they can achieve, so as I said before, check what the car asks for and get one that matches. What it is made of is largely irrelevant.