If you look at the label on a can of oil (unless it's either a top end race oil, some American oils or total rubbish) there will be an ACEA A spec and B spec mentioned. The A spec refers to petrol and B to diesel. Most oils will say something like ACEA A3
3 or A3
4 meaning that they meet the equivalent petrol specs and diesel specs, or are at least close to them. Except in some odd engines, like some generators and a few other random things, you don't get a diesel only oil, you don't just see a B spec on the can.
A lot of it comes down to development costs, why make two oils and pay for one to be tested for ACEA A specs and other for B specs? It's cheaper to make an oil that covers both and then market it as a 'petrol' and 'diesel' version, usually putting a couple of quid extra on the diesel version(Castrol did that with the Magnatec 10w-40 and I'm pretty sure it's the same with the Edge 5w-40 as well). If the name of the oil contains the word 'Diesel', it's only there for customer confidence.
Consider the manufacturer specs like VW504.00 and VW507.00, BMW LL98/01/04, Merc, GM, etc etc etc. Part of the requirement of each spec will be to meet ACEA specs. If you have a BMW from 2008, that car will use an LL04 oil, regardless of whether it's a petrol or diesel. A VW on a long life schedule will use a 504.00 (petrol) or 507.00 (diesel) oil, but with those ones, if the oil meets 504.00, it also meets 507.00 and vice versa.
Some oils have another ACEA spec, the C rating that does relate to diesel engines and if the car needs a C spec oil, you must use one as they are low ash oils, formulated for use in engines with diesel particulate filters. A C spec is part of the BMW LL04 and VW507.00 spec, meaning that they are the oils to use in those cars fitted with the DPFs, but they are also suitable for the petrol engined versions as well.
Cheers
Tim