Not exactly. There are multiple kinds:
1. Scripting language interpreter: these are what you commonly hear about, examples being Python, lua, perl, ruby, etc.
2. Virtual machine interpreter: sometimes programs are written for virtual computers that don't exist, and these let you run programs for them; examples include Java, C#, Z-machine (think ZORK and friends), etc. Note that most of these also come with a JIT that speeds up execution, so you typically won't hear them being called interpreters.
3. CPU emulator interpreter: these are what cause demanding emulators like PS1 to be very, very slow (at least when they're first ported to a new system). An emulator that uses an interpreter looks up instructions one by one, has to figure out what it does, and then simulates its effects. JITs/dynamic recompilers are usually preferred when possible, of course, but for some really old systems, it's not really worth it due to them needing more accuracy than speed, and the tradeoffs aren't worth it.