I think it might be Philadelphus (one of the shrubs given the common name mock orange; it has wonderfully scented white flowers).
(It is also a bit reminiscent of Fuchsia, but I would expect to see at least a hint of pink in the stems.)
I think I can also see Clematis in the background (leafless stem).
'Big white flowers later in the year' - fits with Philadelphus.
The second one looks like Spiraea, perhaps S. arguta, sometimes called 'bridal wreath'. White flowers in fairly dense heads, in convenient 'spray' shapes for flower arranging. (There are others, with pink flowers, either in flat round heads or 'pokers', but I suspect yours is neither of those.)