According to Apple's Time Machine documentation: Time Machine automatically makes hourly backups for the past 24 hours, daily backups for the past month, and weekly backups for all previous months. The oldest backups are deleted when your backup disk is full.
If you are only doing manual backups, then you lose most of Time Machine's functionality. Time Machine doesn't know or care how a backup was made. When it deletes old backups, it uses the algorithm above.
It sounds like your Time Machine drive is too small. Your Time Machine drive should be 3 times the size of all the disks you are backing up. If you have a large amount of data, that can be cumbersome. You can get away with a backup disk that is twice the size of your used storage. So if you have an internal 2 TB drive with 1 TB free, you could probably get away with 2 TB backup drive. But that is strictly "get away with" because you will have problems eventually due to a backup drive that is tool small. Most likely, you will do some big operating system update and Time Machine will complain that it doesn't have enough free space. Don't freak out when that happens, just erase the backup drive and start over.
You may also find plenty of people saying that this "3 times the size" advice is nonsense. Time Machine will work with less. But you can expect to have to erase the hard drive sooner that way. All too often, when this happens, people forget about that advice and go all over the internet posting about how awful Time Machine is. This leads people to not use Time Machine and then lose their data. Ignoring good advice can spread your misery, like a virus, to others.
