There is a lot of confusion about the terminology used by florists but most of the terms are easy to understand with a little help. It is actually the use, binding and setting of the flowers which determine whether they are a bunch, a bouquet or an arrangement.
A bunch of flowers is simply a collection of stems. Elaborate bunches have a few different varieties of flower but simpler bunches can be picked from your own back garden and need only comprise one kind. Bunches of flowers are usually arranged so that they are pleasing to the eye from several angles and so that they sit nicely in a vase but they can also be split into separate vases or trimmed before display.
A bouquet (such as a bridal bouquet) is a careful arrangement of flowers so that their heads are plush in a dome or other shape and so that they can be held or presented on a table without a vase. When making a bouquet a florist angles the heads of the flowers how ever they like in the arrangement and binds them in to that setting with tape, much like a jeweller sets a stone in a ring. The rest of the stems are then trimmed and bound and often finished with ribbon so that it can be held or displayed easily. Details such as pearl-ended pins can sometimes finish off bouquets by affixing the ribbons to the stems.