Of the 'Bekannten Torten' listed on the Wikipedia page here (https://de.m.wikipedia.org/wiki/Torte), some have established names in the UK, eg Black Forest gâteau and Sachtertorte.
In generally I'd call very creamy special occasion cakes, such as the Schwarzwälder Kirschtorte, a gateau.
Pastries with fresh fruit on top are generally called tarts, especially individual one-portion tarts (or tartlets) from a fancy bakery.
Traditionally, open-topped fruit 'Torten' were called flans in the UK (https://en.wikipedia.org/wiki/Flan_(pie). The Erdbeertorte in the Wikipedia pictures I would naturally call a strawberry flan. That's a cake (not pastry) base with fruit and jelly on top. (But not a 'strawberry pie', as the English Wikipedia page for the Erdbeertorte says - that's AE.) Both my grandmothers made lots of fruit flans circa 1990 in the UK. It's probably the last time I had a home-made fruit flan. But 'flan' is a word that makes me think 'grandmothers' rather than 'fancy patisserie'...
Anything spongey, such as a Victoria sponge, carrot, walnut, chocolate, red velvet, lemon drizzle, etc, I'd call cake.
Wedding cakes are traditionally fruit cakes ('fruit cake' is a specific kind of cake made of dried fruit, rather than a generic term for any cake that includes fruit), in three tiers, although Victoria sponge and chocolate cake are also popular. Fruit cake is very dense so the bottom tier is usually fruit cake to hold up the two smaller tiers.
