There is some overlap between the two words, but there is an important difference when it comes to timing.
A possession is something that you possess. This can be legal or illegal. Assuming that what you possess is legal (that is, it is not stolen or forbidden), then you own it and have rights over it. So, if you want to destroy it, you can.
An inheritance will be yours legally at a designated point in time. Usually, it is when someone dies, but not necessarily so. We can say that an inheritance is the act of passing on something - property, titles, and even debts - to another individual. Finally, when you inherit it, then it is part of your possessions.
Possession and Inheritance are two words that have different meaning but are connected.
Possession basically refers to the things or property that we have. In short any thing that belongs to you is your possession. It can be anything like clothes, property, shoes, pets, etc. It can be legal or illegal and you can destroy it whenever you want without telling anyone or asking for permission to do so.
Inheritance consist of other people belongings that you get according to the will of that person living or dead. Can be property, loans etc. When these are handed over to you then they become your possessions that you can keep or do whatever you want with them.
Possession is to have or own or control something like property, ownership, tenure, holding, estate etc.
Inheritance is receiving money, property or a title as an heir at the death of a previous holder. It could also mean to succeed someone.