Most tea brands in the UK have a decaf version e.g. https://www.pgtips.co.uk/our-teas/tastydecaf . It tastes almost the same as black tea although I think I can detect a slight difference. My understanding is that there's a post-process treatment of the leaves to remove the caffeine.
You're right that drinks not brewed from camelia sinensis leaves should technically be called an infusion or tisane. That includes fruit "tea" and infusions like rooibos, chamomile, nettle, or maté. However it's very common even in the UK to say "fruit tea" or "chamomile tea".
Does such a thing exist? Usually "tea" is made from tea leaves and other similar drinks are called "infusions" or "herbal tea" instead. I have never heard of decaff tea, but maybe it is common in other places?