The difference between "These are a few examples" and "These are but a few examples" is the addition of the word "but" in the second sentence. In this context, the word "but" means "only" or "merely". So, "These are but a few examples" implies that there are very few examples, and it may be insufficient to fully illustrate the point being made. On the other hand, "These are a few examples" simply states that the examples provided are just a small sample, without implying that it is inadequate. Both sentences are correct and have similar meanings, but the use of "but" in the second sentence adds emphasis to the fact that the examples provided are limited.

It's the same as the difference between "She is six years old" and "She is only six years old"

Both intend to communicate that you will be giving some examples. However, when you say "these are but a few examples" you are emphasising the fact that there a LOT of examples, but you are only mentioning a few.