This is a common question I get asked and it's not as simple to answer as you might expect, but please keep with me.
Lubricating oil properties are derived from a combination of the base oil used and the additives used to enhance or remove certain desirable/undesirable characteristics. There are 5 groups of base oils – there are no good or bad groups and all the base oils have their purposes for different industries and applications. Groups 1 and 2 are mineral oils, and tend to be good solvents in removing contamination, dissolving varnishes etc, but do not tend to last as long – these tend to be the cheaper oils on the market when marketed as such and if you are changing oil regularly can be a good choice of lubricant. However cheap doesn't necessarily mean nasty as some of the premium aftermarket solutions for e.g. removing varnish from systems are based on group 1 oils. Group 2 is a more refined and purer version of group 1.
Group 5 are synthetic oils meaning they do not come from crude oils, and all the miscellaneous products that don’t fit in other categories such as biodegradable oils, vegetable oils and fire resistant fluids etc are all classed in this category.
Group 3 is a highly refined mineral oil, and group 4 is man-made (i.e. synthetic) oil by linking together smaller chain molecules to make the oil. The top end of group 3 oils and group 4 oils are chemically identical so that no lab can tell the difference – so much so, court rulings in some countries rule that group 3 is so pure that even no not synthetic in the sense it is man-made, it should be given the status of synthetic because it is so pure to match the properties of a group 4.
Hence, when trying to determine if something is mineral or synthetic the question should be phrased.
Can you tell the difference between groups 1 or 2 with 3/4/5 then the answer is yes.
If the question is determine if group 5 vs 1 to 4 then again the answer is yes.
However, if groups 3/4 then the answer is likely to be No, but if the oil is from either of these base stocks the performance is expected to be very similar anyway.
I would hence try to move away from traditional buying an oil because it's synthetic or mineral and move to what performance improvements the lube oil provides for the cost instead.
If you need help in selecting your lubricants your lube oil suppliers will be happy to help, but comment below if you still have any questions or want some independent advice.