What is the difference between the right to assemble and the right to petition?

Answer 1

The right to assemble means 3 or more people may gather together and discuss what they wish - when it is denied such a gathering is call a riot or a conspiracy and the people involved are arrested.
The right to petition means that a group of people may write up their complaints and take them (usually signed) to the government for requesting a change. Where the right to petition is formalized, certain number of signatures from identified voters - perhaps 5% of the voters in the last election or 1% of the population - is required if if met, the request on the petition must be put on the ballet for everyone to vote on in the next election. Petition may also be used in some cases to remove an elected official from office - usually a much higher percentage than to put it on the ballet.