Every drummer looks for a specific sound that they are wanting out of their kit. Yes, putting a specific head on your drums will alter the sound, but I have met plenty of drummers cycling through heads trying to get their kit to sound a way that it just can't produce. The best video I could find to help represent the differences is from DW drums, which by the way, an excellent choice for a kit. In this video, DW compares 4 of the different types of woods used for shells. Below the video, I have described the differences between the types of woods used in drum shells.
Maple is the most popular and most common type of wood used for drum shells. Maple has even mids and highs, while having soft lows.
Birch has great high-end and a very punchy low-end, while the midrange is a little quieter. Birch is the best drum shell for annoying your neighbors as it is loud.
Beech has defined midrange and highrange, with a punchy low-end.
Mahogany has a very warm sound with quiet highs, and a warm midrange and low-end.
Oak has warm highs, midrange, and low-end. Rapid decay on ring out.
Walnut has equal amounts of highs, midrange, and low-end and is very big sounding.
Cherry has a lot of highs and a lot of punch in the midrange. Bright tone is a good way to describe cherry.
Ash has defined highs and midrange, and it is very warm sounding.
Knowing the different woods that are available for drum shells can help you achieve that sound you are searching for.