Building regulations: where it gets more specific
This is the area where conservatories and orangeries genuinely differ from each other, and from a standard extension:
A conservatory can be exempt from building regulations if it meets specific conditions: it's built at ground level, has a floor area under 30 square metres, is separated from the house by external-quality doors or windows, and has either an independent heating system or no heating at all. Roof and wall glazing ratios also come into it, a structure with a substantially glazed roof and thermally separated from the house is more likely to qualify for the exemption.
An orangery, because it typically has a more solid, part-brick construction and a largely flat or lantern roof rather than a fully glazed one, is usually treated as a standard extension for building regulations purposes and needs full approval covering insulation, foundations and electrics.
The exemption disappears for either structure if you remove the internal doors between the house and the new room to create an open-plan space, which is an increasingly popular design choice, since at that point it's functionally part of your heated living space rather than a separate room. We'll tell you clearly at the design stage whether your specific plan qualifies for the building regulations exemption or not, since it affects both the process and the specification.