D/s is a subset of BDSM. BDSM encompasses a much wider variety of activities, including, but definitely not limited to D/s.
D/s refers specifically to dominance and submission, which, itself, can play out many different ways, but always involves one partner specifically in control of the other. This is usually considered to be distinct from one partner being in control of the scene itself - typically, when one describes a scene as D/s, especially in that capitalization form, it refers to one partner being directly in control of the other partner. D/s usually refers to some form of servitude, bondage, or fetish worship, but this is not an absolute requirement.
BDSM is an acronym (most correctly a compound initialism) that refers to:
- Bondage and Discipline (BD)
- Dominance and Submission (DS)
- Sadism and Masochism (SM)
...or any combination of the above. It encompases a VERY wide variety of play, and is generally synonymous with the term 'fetish' (they technically mean different things, fetish being the sexualization of a specific concept, but are used interchangeably by the community). Basically anything 'kinkier' (kink being an even broader term, encompassing anything considered sexually explicit, though again it is also often used interchangeably by the community) than anal sex falls in some way into fetish/bdsm.