I was curious if it was possible to separate such liquids e.g. two vegetable oils that happened to have different ingredients, so it is a different liquid, but the same density etc.
Typical vegetable oils are not just one chemical compound, but a mixture (after removing everything that is not) of glyceride triesters. The chance that there is some overlap between your two oils is big, so the answer to your immediate questions likely is no, completely impossible.
Even if there is no overlap in the chemical composition, you would probably still have to separate the oil mixture into all its components, and then know how to mix them together again to get the original two oils.
The latter is possible, of course, with a reasonable analytical effort, the former is close to impossible to perform on a macroscopic sample. A GC(-MS) can easily separate (and identify) the compounds, but that's a few billion molecules or so. Doing liquid column chromatography would be very tricky, with any reasonable apparative effort would give you a few milligrams of each compound, and perhaps there are still a few you can't separate.
Distillation is impossible (boiling points are high and too similar), fractionation by crystallisation would only work well for some of the triglycerides, etc. All in all it's a bad mess. Don't mix two oils and try to separate them afterwards. ;-)
By saying that you have different materials ("different ingredients"), an analytical technique which shows a difference could be scaled up to effect a separation. Density was rejected as not giving a difference; chromatography was not recommended (but might work).
The problem with two (different but very similar) vegetable oils is that they are not simply two different materials, but rather two different mixtures of very many of the same or similar compounds. If you could separate the compounds in the mixture (e.g., by chromatography), then you would have to figure out how to apportion the separated individual compounds to form mixtures like the original oils.
In the 1970s, Canadian farmers grew strains of rapeseed with significantly lower amounts of (toxic) erucic acid through crossbreeding. The new plant was called canola, suggesting “Canadian oil, low (erucic) acid.” Canola oil and olive oil are vastly different in source and manufacture, although their composition is similar (from Wikipedia: Saturated fatty acids: 7.4%/13.8%; Oleic acid: 61.8%/71.3%; Linoleic acid: 18.6%/9.8%; smoke point: 238 C/193 C.).
Now if you mixed canola oil and olive oil, you could determine the proportion of each by analysis of all the constituents, but as far as separating the individual compounds and reconstituting the original olive and canola oils… Nah, I don’t think so.
On the other hand, two practically identical materials might be separable if they were only single entities. For example, H2O and D2O are regularly separated even though they are very similar.