Possibly - and 'redwood' as with many timber terms is pretty vague. But I note that:-
1 - redwood from a redwood tree (as per USA giant trees) is a softwood - and really is quite soft and dusty. It is also more pinkish than red (see attached pic of a sawn sample I have). Do softwoods have burr?
2 - your pic looks a bit like timber plausibly sold to me as 'red mallee' which is burr from an Australian eucalyptus small tree/bush. See pic. But many other burr timbers might look similar (indeed I think 'mallee' can be a number of species).