I was casually browsing wikipedia the other day and I came across a page called "Kingdom of Germany", and by the looks of it the Kingdom of Germany is an actual nation. However, that page did make note that the Kingdom of Germany was inside the Holy Roman Empire, so this is where it gets confusing for me personally. The Holy Roman Empire (was considered) as a nation right? But the Kingdom of Germany is also a nation, which nation did the people live there identify with? In other words, did the concept of a unified Germany already exist in that time? (800s) Or is the Kingdom of Germany just another way of saying Holy Roman Empire and in reality they are the same thing?
Hi!
I would like to preface this answer that in order for one to understand the concept of Kingdoms in the early (800s) to late (1400s) middle ages, there is a need to decouple the concept of a modern nation-state to actual titles. This distinction is needed so that it is easier to understand that within the medieval time, there is no concept yet of a German nation as established by Westphalian conventions, but what is available is the concept of a large area of land, usually called by the Romans as Magna Germania or Greater Germany, that shall have a king, but not necessarily have all the trapping of a modern state like a central revenue collection service (IRS), or even that of a single unified military force. What the king does instead is essentially rule over/have friendly relations with a bunch of local lords who are usually Dukes at this time, who rule over smaller parcels of land within that larger area of land called Magna Germania.
So to say that the Kingdom of Germany as a nation existed in the Middle Ages is quite problematic at best and fallacious at worst.
To showcase the gravity and the potentially complexity of this perspective, I went to the "Kingdom of Germany" wiki page and wasted 7 hours reading through all their arguments and sources in the talk page lightly checked the page itself, and the points I raised in this answer are all actually raised as well on that wiki article's talk page, and it is currently in discussion on how to revise the current page as it is to shift it away from a potentially confusing perspective.
However, it is true that at certain points in time, the title "King of the Germans" was indeed used, discarded and renamed within the history of the Holy Roman Empire, usually to denote the elected successor of the Holy Roman Emperor as with Conrad II crowning his intended successor Henry III as King of the Germans.
Neither were "nations". They were feudal realms with hardly any concerns for ethnic nationalities.
The kingdom of Germany was the continuation of the 843 by the division of the Carolingian empire created kingdom of East Francia. Names for states changed a lot over the course of centuries. By the mid 11th century the term "Regnum Teutonicum" or "Regnum Teutonicorum" (roughly "German kingdom" or "kingdom of the Germans") became more common than the older "regnum francia orientalis".
The German kings starting with Otto I. conquered the formerly independent kingdoms of Italy and Burgundy and made them de jure part of their inherit kingship. Still those kingdoms nomally stayed separate for a while, having their own set of laws and chancellories but one king.
On top of that they started getting crowned "emperor of the Romans" by the pope and thusly simply started to refer to the entirety of their dominions as the "(Holy) Roman Empire" which was actually supposed to be the continuation of the original Roman Empire.
Their royal title wasn't descriptive in the beginning (10th to 11th century). They simply called themselves "by the grace of god king". But foreign diplomats needed to address them somehow and this is were the term "rex teutonicorum" (king of the Germans) came to be (originating in Italy). It wasn't meant as anything provocative at first but pope Gregory VII began using it as such in order to diminish the German kings' supranational importance and their claim to the imperial crown. That's when the term "rex Romanorum" (king of the Romans) began being used officially.
For the most part there wasn't really any difference between the kingdom of Germany and the empire at large. If anything the kingdom was treated as an administrative area of the empire, nothing more. There weren't any German kings separate from the emperor aside from some anecdotal evidence (Frederick II referring to his son as "rex Alamanniae").
From 1508 onwards the official title of any crowned emperor was "Imperator Romanorum, Rex Germania" (emperor of the Romans, king of Germany) but it's not sure that "Germany" meant anything but the area of the HRE at that time.
TL;DR:
Yes, the "kingdom of Germany" existed as a notion inside the Holy Roman Empire but it was largely meaningless.