No, the statistics are the same.
As found in Equipment – Weapons In the PHB, if a weapon is made of unconventional material or construction, this will fall under Improvised weapons:
An improvised weapon includes any object you can handle in one or two hands, such as broken glass, a leg of a table, a pan, a wagon wheel or a dead goblin. Often, an improvised weapon is similar to a real weapon and can be treated as such.
So a club is a club, regardless of whether it's a bone or metal club, the statistics are the same. Looking at the list of Weapon properties (Finesse, Heavy, etc.), different materials are not listed and, therefore, this does not affect the statistics themselves. Depending on the weight of the materials you use for your club and other weapons, you might consider them heavy or light:
Heavy: Small creatures have disadvantages in attack rolls with heavy weapons. The size and volume of a heavy weapon make it too large for a small creature to use effectively.
Light: A light weapon is small and easy to handle, so it is ideal to use when fighting with two weapons.
The only material specifically mentioned in the PHB is for Silver weapons, which allows players to damage certain creatures that have immunity or resistance to non-magical weapons:
Some monsters that have immunity or resistance to nonmagical weapons are susceptible to silver weapons, so cautious adventurers invest additional coins to wield their weapons with silver.
At the DM's option, a character dominating a weapon can use a similar object as if it were that weapon and use its ability bonus.