That's not the way it works, there are no general rules and you cannot assume much. It's certainly not a given that a medium to large suitcase is always allowed free of charge (whether as cabin luggage or checked in to the hold). There are also many things you just cannot take with you as a regular passenger and thresholds you cannot exceed even if you are ready to pay a fee.
The 23 kg limit is something else, it's a recommended threshold for health and safety reasons as handling heavier weights all day long is dangerous. But some airlines will have a lower limit or won't allow any hold luggage without an extra charge. Others will let you take more than 23 kg of luggage as a matter of course provided it's spread among several bags and many will have different rules for different routes (and/or fares). Many also have a higher “hard” threshold and allow luggage up to 30 kg (e.g. for business class passengers or for an extra fee).
When considering a flight or holiday, you therefore have to look for information regarding the specific rules that apply to that specific airline, fare, or package.