When you say "type" I'm going to assume you mean static type mostly. But I'll talk about dynamic types shortly.

A static type is a property of a portion of a program that can be statically proven (static means "without running it"). In a statically typed language, every expression has a type whether you write it or not. For instance, in the Cish "int x = a * b + c - d", a,b,c,and d have types, a * b has a type, a * b + c has a type and a * b + c -d has a type. But we've only annotated x with a type. In other languages, such as Scala, C#, Haskell, SML, and F#, even that wouldn't be necessary.

Exactly what properties are provable depends on the type checker.

A Scala style class, on the other hand, is just the specification for a set of objects. That specification includes some type information and includes a lot of implementation and representation details such as method bodies and private fields, etc. In Scala a class also specifies some module boundaries.

Many languages have types but don't have classes and many languages have classes but don't have (static) types.

There are several observable differences between types and classes. List[String] is a type but not a class. In Scala List is class but normally not a type (it's actually a higher kinded type). In C# List isn't a type of any sort and in Java it's a "raw type".

Scala offers structural types. {def foo : Bar} means any object that provably has a foo method that returns a Bar, regardless of class. It's a type, but not a class.

Types can be abstracted using type parameters. When you write def foo[T](x : T) = ..., then inside the body of foo T is a type. But T is not a class.

Types can be virtual in Scala (i.e. "abstract type members"), but classes can't be virtual with Scala today (although there's a boilerplate heavy way to encode virtual classes https://wiki.scala-lang.org/display/SIW/VirtualClassesDesign)

Now, dynamic types. Dynamic types are properties of objects that the runtime automatically checks before performing certain operations. In dynamically typed class-based OO languages there's a strong correlation between types and classes. The same thing happens on JVM languages such as Scala and Java which have operations that can only be checked dynamically such as reflection and casting. In those languages, "type erasure" more or less means that the dynamic type of most objects is the same as their class. More or less. That's not true of, e.g., arrays which aren't typically erased so that the runtime can tell the difference between Array[Int] and Array[String]. But remember my broad definition "dynamic types are properties of objects that the runtime automatically checks." When you use reflection it is possible to send any message to any object. If the object supports that message then everything works out. Thus it makes sense to talk of all objects that can quack like a duck as a dynamic type, even though it's not a class. That's the essence of what the Python and Ruby communities call "duck typing." Also, by my broad definition even "zeroness" is a dynamic type in the sense that, in most languages, the runtime automatically checks numbers to make sure you don't divide by zero. There are a very, very few languages that can prove that statically by making zero (or not-zero) a static type.

Finally, as other's have mentioned, there are types like int which don't have a class as an implementation detail, types like Null and Any which are a bit special but COULD have classes and don't, and types like Nothing which doesn't even have any values let alone a class.