Difference between filter and choice in camel

What is the difference between filter and choice in apache Camel?

    from("direct:a")
        .choice()
            .when(header("foo").isEqualTo("bar"))
                .to("direct:b")
            .when(header("foo").isEqualTo("cheese"))
                .to("direct:c")
            .otherwise()
                .to("direct:d");

In short a filter is like a single java if statement, eg

if x = 2 {
  ...
}

And in Camel:

.filter(header("foo").isEqualTo("bar"))
  ...
.end()

And choice is like a java if ... elseif ... elseif ... else statement,

if x = 2 {
  ...
} else if x = 3 {
  ...
}

And in Camel:

.choice()
  .when(header("foo").isEqualTo("bar"))
    ...
  .when(header("foo").isEqualTo("chese"))
    ...
  .otherwise()
    ....
.end()

Note that otherwise is optional in the choice.