A Record<K, T> is an object type whose property keys are K and whose property values are T. That is, keyof Record<K, T> is equivalent to K, and Record<K, T>[K] is (basically) equivalent to T.
K has a purpose... to limit the property keys to particular values. If you want to accept all possible string-valued keys, you could do something like Record<string, T>, but the idiomatic way of doing that is to use an index signature like { [k: string]: T }.
It doesn't exactly "forbid" additional keys: after all, a value is generally allowed to have properties not explicitly mentioned in its type... but it wouldn't recognize that such properties exist:
declare const x: Record<"a", string>;
x.b; // error, Property 'b' does not exist on type 'Record<"a", string>'
and it would treat them as excess properties which are sometimes rejected:
declare function acceptR(x: Record<"a", string>): void;
acceptR({a: "hey", b: "you"}); // error, Object literal may only specify known properties
and sometimes accepted:
const y = {a: "hey", b: "you"};
acceptR(y); // okay