Thrift shop

This is really two questions. I've therefore tried to answer them separately.

For the first example I would disagree with SimonPoole here, as I see variety stores as selling keenly priced new goods in a selected number of discrete categories. I've had a quick look on taginfo and there does not seem to be an obvious tag. In the UK the second hand market is completely dominated by charity shops, so tagging for-profit shops has not been very important. Historically these might have been called junk shops. A few do exist in my local area and are mainly tagged shop=recycling, but this is very much a 'placeholder' tag as most call themselves "Recycle Shop".

I wouldn't see shop=thrift as being out-of-place (there are 4 already), it's American English but I think a well understood meaning. shop=second_hand would be more explicit, but second_hand=yes is a more generic tag and may result in conflicts. A discussion on the tagging mailing list might produce a consensus for which tag to use in the future.

Summary: there does not appear to be a well-established tag for this type of shop, and a range of values have been used at the local level. I would avoid shop=variety or variety_store as this may change its existing meaning.

Your second kind of store probably sells in a given category such as clothes, and if so can be tagged exactly as any other clothes shop. The usual terms for such shops are outlet or factory stores. There are numerous shopping centres throughout Europe dedicated to such shops: e.g. Cheshire Oaks, Bicester Village, Clark's Village and numerous ones around Mendrisio (CH) such as Fox Town. I can't find a tag in use which delineates such shops from mainstream clothes shops. An old classic example would have been Filene's Basement.

If the store sells in multiple categories then I am in agreement with Simon's suggestion as the best fit. Again some additional tag would be useful.

Summary: either use the main category of goods sold (clothes, furniture, sports etc) or if a range of goods in different categories then use variety_store.