The difference between conventional and non conventional current is that, conventional current is a direction of flow of positively charge particles and non conventional current is a direction of flow of negatively charge electrons ( in opposite direction) under the influence of electric field.
For further knowledge, find in attach, a paper on this concern.
Conventional catalysts are the catalysts that are commercially available while nonconventional are no available commercially. Nonconventional catalysts are rationaly designed for a specific purpose, mostly for reactions where conventional catalysts are not suitable. You can go through my articles for detail understanding.
Yes, as Peter Alaba mentioned Conventional catalysts are the catalysts that are commercially available while nonconventional are no available commercially.