Chardonnay is always white wine made from chardonnay grapes, but exactly where the grapes are grown, how the wine is made, how it's aged and what types of barrels are used in aging produces characteristics that can make one chardonnay taste very different from another. Those characteristics don't fall neatly into a "type" category, except whether it is "unoaked" (stainless steel barrels, no exposure to oak, cleaner, crisper flavor)
yes, oaked chards are aged in oak barrels (french oak, american oak or a combination of each) can have a really buttery feel along with a woody taste...you will get a little fruit flavor from this but mostly vanilla and the like. the different woods add different characteristics to the wine. unoaked chards are aged in stainless steel barrels and produce a much crisper wine than those aged in oak. you will get more pear and apple flavors from a wine like this.
this is a very short explanation. wine is very complex!!!