If you're interested in paradigms, the paper Programming Paradigms for Dummies: What Every Programmer Should Know covers them.
In functional programming, state is implicit - the program executes by calling functions which call other functions. In imperative programming and object oriented programming, state is explicit - you change the value of a variable or object's field.
In a way, functional and imperative systems can be seen as duals - what's fixed in one is a dynamic value in the other.
Closures - which trap some explicit, mutable state in an object which can be called as a function - sit somewhere between, being neither pure functional programming but not quite fully fledged objects; they are more like anonymous objects than functions.
'Dynamic languages' is vague term, usually meaning one of the following:
Dynamically Typed Languages - languages which delay determination of type to runtime, but the set of types is fixed. Examples are Smalltalk, Lisps, current Fortress implementations. Some otherwise statically typed languages also allow some dynamic type checks - Java, C#, C++ and Ada. ( it was a failed dynamic type cast from float to int in Ada that crashed Ariane 5 )
Languages with dynamic types - languages where new types can be created at runtime. The most popular is JavaScript. Because you have to run the program to determine the types, it's harder to make IDEs for these with type aware autocompletion.
Languages which are dynamically compiled - languages where new scripts can be compiled at runtime. This is true of bash, JSP, PHP and ASP at the page scale, and true for at a finer scale for lisps and JavaScript which support an 'eval' function which compiles and runs an expression.
Functional languages which are strongly typed often perform a large amount of type inference, so it's common for their programs to have less explicit typing than poorly implemented static typed languages. This can confuse people who have only seen the lack of explicit typing in dynamic typed languages into believing that type inference is the same as dynamic typing.