Does using Time Machine require external hard drive?

I use my laptop for very basic things (personal documents, financial stuff, etc.) and I never really understood how Time Machine or Time Capsule worked, so (don't judge me too harshly) I have never set it up or done a backup before. Long story short, I am recognizing this shortcoming and want to remedy it going forward but I am still a little unsure of myself... from what I have read about backing up your Mac using Time Machine, it seems to require that you choose where to store the back up, and more specifically, somewhere external (hard drive, USB, etc). But I have seen mentioned online that there is a way to "partition" and store the back up without an external drive. Is that a thing? If not, and I do need to buy a hard drive or USB to capture the back ups, is there a more optimal choice you would recommend? If I use one of these, I assume I need to back it up manually since it needs to be connected? Is there a way to automatically back up and I am just missing the basics here? Thanks in advance for helping me navigate this!!