I suspect the question and answer are from an older textbook, because the Full Format process has been changed in the most recent versions of Windows.
Initialization is slightly better than Formatting. In fact, the process of preparing a HDD to accept data has two steps. The first is Partitioning. Creating a first Partition does three things: it writes a Partition Table to a specific location at the beginning of the HDD; if the HDD unit is to be bootable, it also writes a Master Boot Record (aka MBR)for an older Partition style (or a more complex Partition Table and boot loader code for the new GPT style of Partitioning); and, it writes to the first record of the new Partition Table the parameters of the Partition it is creating. A HDD can have up to 4 Partitions in the old MBR system, and many more in the new GPT system - depends on the structure of the Partition Table created.
After the Partition Table is created, the second step is then to Format that Partition. This process writes to the beginning of that Partition the files needed to establish and operate the particular File System you choose - these days, usually NTFS. These include the Root Directory, a File Allocation Table that tracks exactly which Sectors of the HDD are used by which file (the NTFS system has a much more complex file for this) plus a few other system files used by the selected File System. The last task of this is to write zeros as the "data" in those system files. Now, the Format process has two possible versions. A Quick Format establishes the system files and zeroes them, then quits. A Full Format does that, then tests the entire HDD for faulty Sectors by writing a particular data pattern to each Sector, then reading it back to ensure it's right. If any Sector is faulty, Windows writes a record of this to its own on-disk file so that the faulty Sector will never be used. Since the Full Format must do this process for every Sector of the HDD, it takes a long time. Beginning with one of the later Service Packs for Win XP and in all later Windows, these two (Partition and Format) were combined into one wizard to make it easy, called Initialize the Disk. So that's where part of your text question orginates. The most recent Windows now call these combined processes "Create a New Simple Volume".
These prcesses together prepared the disk for use by an Operating System. They establish a Partiton Table with details of a chunk of HDD space that is to be used as one storage resource or "Drive" with its own letter name, and space in it for specifying up to three more Partitions on this HDD unit if there is any space not yet assigned to a Partition. Then they created the specified File System on that one Partition, and now Windws can use that Partition. You can Create other Partitions and Format each of them if the HDD has any spare space, and these subsequent actions will not damage any data on the existing Partitions. Each Partition will be recognized by Windows as one separate "Drive" with its own letter name.
At a later time you can choose a "Disk" (really, a Partition on a HDD unit) and Format it again. A Quick Format will alter (in a predictable manner) the old data in the Root Directory and File Allocation Tables, but leave the rest of the Disk's Sectors untouched. A Full Format will also do the complete Sector Testing process. BUT it is THIS process that has changed recently, and why I say the textbook may be out of date. In Windows XP and previous Windows, if the Full Format was being re-done on a disk that contained data, the Sector testing was in four sub-steps: read and store the existing data, write the new test pattern, read it back and check it, then restore the original data. Thus, that version of Full Format did NOT remove any prior data. Beginning with Win 7 (maybe before that with VISTA, I'm not sure)the Full Format suhb-steps were changed. It no longer reads the original data and later restores it. Instead, it skips the read and, after verifying good testing of the Sector, fills that Sector with zeroes. It also ensures that the Root Directory and File Allocation Table are overwritten with zeroes. Thus the Full Format process in recent Windows versions actually destroys all the original data in all the Sectors of that Partition.
So to recap, up to XP (or maybe Vista), a Quick Format of a Partition would alter the information in the Root Dorectory and File Allocation Tables, but leave everything else untouched. Good software and some skill by an operator could actually re-discover almost all of the files from the unaltered areas of the Partition and re-construct those two major index files so that almost all the original files could be recovered. In those verions of Windows, even a Full Format left the orginal data unaltered, so the files also could be recovered. On the other hand, if you did a Partition operation only, the information in the Partition table (which gives details of where the Partiton(s) are and hence where to find each Root Directory, etc.) is re-written with zeroes and a new location for the first Partition. This makes it more difficult to re-establish the locations of the Partition(s) and start file recovery. If you did a complete Initialization (which is both a new Partition and a Format operation on the first Partition just created), a LOT of data would be zeroed out, making it very difficult to find any old files. BUT, not impossible. There are a lot of people who have rescued themselves from disaster by using sophisticated File Recovery software to get most of their files back after mistakenly re-Initializing or Formatting a HDD.
HOWEVER, the answer your textbook prefers is not so applicable to the newest Windows versions. In them the Initialization process (combining Partitioning and Full Formatting) would zero out not only the Partiton Table and the File System data, but also overwrite all the old data in every Sector of the Partition with zeroes! That make it exteremely difficult to recover any data at all (well, at least from the first Partition if the HDD has more than one Partition). While there are sophisticated software tools that can recover a lot of data even from Sectors overwritten with zeroes, they are very complex, expensive, and time-consuming, so no average user would ever obtain and use such tools. For the most recent versions of Windows, then, the added removal of Partition Table data by using full Initialization instead of only Full Formatting would make little difference to the ability to recover old files.