It is indeed a confusing/confused website as well as grammatically challenged in English. Under 'Before flying':
Hand baggage
The hand luggage that can be carried aboard must have maximum dimensions of 55 X 40 X 20 CM. Its weight depends on the fare purchased on legs Vienna-Verona, Munich-Verona, Frankfurt-Milan Bergamo, Frankfurt-Verona, Munich-Florence, Munich-Bari, Munich-Venice and all seasonal flights:
LIGHT fare: 1 hand baggage (7kg)
PLUS fare: 1 hand baggage (10kg) + briefcase or laptop
EMOTION fare: 1 hand baggage (10kg) + briefcase or laptop
For all other flights from/to Munich (except for Munich-Verona, Munich-Florence, Munich-Bari and Munich-Venice flights) and from/to Frankfurt (except for Frankfurt-Milan Bergamo and Frankfurt-Verona) hand baggage does not have to exceed 8 KG in weight.
It is also possible to carry onboard objects of small dimensions such as:
- 1 handbag or similar
- 1 coat or overcoat
- 1 umbrella or walking stick
- 1 small camera
- magazines/books
- 1 handbag and baby food to use during the flight
All luggages that exceed these indicated dimensions must be stored in the cargo hold and handed in upon check-in.
The hand luggage can be carried with no additional fees. For safety reasons and for the limited space in the overhead compartments, it is not possible to carry more than 1 luggage aboard.
Further down on the page the 'Carry on baggage and check baggage allowance' section is entirely about checked baggage (which is probably just as well) and it looks like the higher allowance for HON/SEN only applies to checked baggage.
I like the idea of EMOTION fare.