"Reply" will add the relevant post and put it straight into the reply box at the bottom of the page ready for the member to type in a response
The "Quote" works slightly differently as it adds it to a separate quote list. Pressing the "Quote" button once will add the post to the quote list and clicking it again will remove it (hence toggle)
At the bottom of the page next to the reply box you will see an "Insert Quotes" which will reveal the list of quoted posts and gives the option to add them to the reply