Since both are common names that apply to several lily species, feel free to call it whatever you like :-)

It is most likley to be a selection of either L. lancifolium (used to be L. tigrinium, hence 'tiger lily') or L. superbum (what is usually called 'Turk's cap') - the flowers are almost identical in appearance but one is a native species and somewhat rare these days and the other is an Asian import. The import - lancifolium - will have black bulbils produced along the stem in the leaf axils. The native does not.

I think I see bulblis in your first photo so I would assume this is Lilium lancifolium.

Yep, it definitely has the black bulbils all along the flower stalks. OK, I hadn't realized that's the primary visual difference between the two. Thanks for that.