There are two of “The Memory Book” one by Harry Lorayne, and the other by Tony Buzan.
I am going to assume you are talking about the one written by Harry Lorayne. It’s an old book but I still have it in my library along with the other one written by Tony Buzan.
Pegs are pre-memorised, they don’t change, and used for storage and retrieval of the items you want to memorise, but with no locations.
Memory palaces are also used for storage and retrieval but with using locations instead. You can use your memory palace for either short term, or long term by spaced repetition.
The peg system is very useful to memorise a quick list of items such as a to-do list, shopping list etc. However it’s more powerful when used with locations.
You can use the peg system and place the links into your memory palace. For example, when we memorise number digits, we are in fact using the peg system with pre-memorised pegs, and we place them into the memory palace.
We can then use the same pegs in another memory palace to memorise some other information.
If you don’t use a memory palace, then you’d be blocking the pegs with the information already attached to it, unless otherwise they are used short term such as your to-do list of the day, and re-use them the next day, or unless you just want to use those pegs to limit yourself with the into attached to them which is not really ideal.
Have a quick look at this post where I go into a little more detail into the peg system. At the end of my post, I do mention that I always place my pegs onto the locations in my memory palace.