Why did the EU adopt another terminology (i.e. subsidiary protection) for non-1951-Convention refugees? Does subsidiary protection confer fewer right in practice than refugee/asylum status under the 1951 Convention? Or is it a distinction without a (practical) difference?
EU law typically aims at “harmonising” (that's the technical term) national law and does it in several ways. Regarding asylum, it's only a partial harmonisation, defining a minimum set of rights which member states can build upon but not ignore. Importantly, before this harmonisation effort, EU member states already had different regimes, with some states readily granting refugee status to people fleeing armed conflicts (and therefore going beyond the UN convention definition) and others preferring ad hoc national protection regimes. The EU directive retains both through this concept of “subsidiary protection”, presumably because some member states would not have accepted an extension of the refugee definition.
There are indeed important practical consequences. For example, the family reunification directive gives some rights to refugees (forbidding states to impose accommodation or income requirements for family reunification) which do not automatically apply to people benefiting from subsidiary protection. Similarly, the protection from criminal prosecution for crossing a border irregularly that exists in the 1951 convention and in the EU asylum directive only applies to refugees. Both refugees and people benefiting from subsidiary protection have access to the job market and to some welfare benefits, but only refugees must be granted benefits on a par with other legal residents. Refugees' residence permit have to be valid for three years, whereas permits for subsidiary protection only have to be valid for a year.
Importantly, the EU directive does not prevent a state from providing more extensive rights to people under subsidiary protection nor does it prevent states from treating anyone as a refugee even if they do not meet the more restrictive definition. So in some countries, this distinction does not have many practical consequences whereas in others it does. Interestingly, if you look at Eurostat's data for first instances decision on asylum applications in 2018, you will see that most EU countries grant some form of protection to 40-50% of applicants but the specific status granted varies widely.
Finally, note that even for refugees, there are differences between the concrete rights granted by the UN Convention and those defined in the asylum directive. The directive acknowledges the convention but does not repeat or further spell out some of the convention rights (which still apply in principles but aren't anchored in EU law).