Is there a collective name for pieces of metal that hold wood together?

In my local hardware store the aisle which displays these is labeled fasteners.

This term however does not distinguish fasteners for joining wood to wood from fasteners which join a wider range of materials.

Joinery is a woodworking-specific term describing various techniques for joining wood pieces together. It does include techniques that use no fasteners, like dovetail joints. However if you're discussing hardware and refer to e.g. "a selection of joinery" it should be commonly understood to mean "a selection of fasteners used in (woodworking) joinery". In the right context it would even exclude glue and other non-metal adhesives, which can also be used to join wood.

In British English they are often referred to as fixings, but this is not restricted to their use with wood, it also applies to their use in masonry, metal work and so forth.

You can see the British hardware store B&Q's catalogue for fixings, here.

Here is the definition of fixing from the Oxford Dictionary Online:

fixing Pronunciation: /ˈfɪksɪŋ/

NOUN

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1.1 (fixings) British Screws, bolts, or other items used to fasten or assemble building material, furniture, or equipment:

'masonry fixings'

'bikes can be mounted on roof bars with special fixings'

More example sentences

'There are also front screw fixings for securing to a back panel.'

'All three 48 x 20 x 41 cm cases use thumb screws instead of conventional fixings.'

'The arrangement and integrity of the rafters, wattles, battens and fixings in most of the buildings with medieval thatch suggest that their base coats were applied when the buildings were first constructed.'

I would use a term like "nails and screws". It's not all-encompassing, but it does convey the idea, and I think it's more intuitive than trying to use a term like "fasteners" which isn't a common idiom. That is, if you asked your neighbor if they had any wood fasteners they would probably give you a funny look, whereas if you asked if they had any screws or nails they would probably offer you that old can of random pieces everybody seems to have on their workbench.