The lubricant in all types of grease is plain old oil. The thickener used to make it stay put in whatever application where it's used is called "soap". The difference in various types of grease is the thickness and the melting point of the soap. General purpose chassis grease has a thin, low melting point soap that's not suitable for applications where high temperatures might be encountered. Older styles of wheel bearing grease had a medium-temperature soap that could handle the temperature rise of a drum brake system. Since disc brakes run at noticeably higher temps than drums, bearing grease suitable for disc brake applications must have a higher melt point, hence the "DB" rating. DB grease is overkill for the older drum brake hubs, but there's no problem with using it there.
Jerry