The short answer is: Yes, it does make a difference what kind of container is used for ageing. The taste will be different.
Winemaking has its fashions and trends, just like any other business. Some of the fashions and trends are maybe of the rather obscure kind. But if you look at it in detail, it can be both fascinating and very important for the character of the wine.
What kind of container does the winemaker store (or age) the wine in before it is bottled? Most people might think of oak barrels or steel tanks but there is a plethora of choices for the winemaker.
Stainless steel is probably the most popular tank. It is easy to maintain and clean. It lasts a long time. It is easy to keep at the correct temperature.
But there are plenty of other options. Oak barrels, as I mentioned, although only a tiny fraction of the world’s wine production is aged in wooden casks. A dozen or so years ago it became fashionable for winemakers to go back to concrete tanks. They had better “thermic inertia”. Then came a period when everyone wanted to try the egg-shaped (yes!) concrete tanks. They kept the lees in constant movement and contributed body, it was said. Currently, it is the era of amphorae and clay jars, the “original” container for making wine, popular not least by the “natural” wine enthusiasts. And there are many more options, different materials, sizes, shapes…