Grice's maxims came first. Leech expanded his maxims further.
Grice's maxims were principles by which we can make a conversation work: say the right thing (Quality) don't say too much, or too little (Quantity), say it at the relevant time (Relevance) and in the way that's understandable (Manner), and these maxims are under the umbrella of the 'Cooperative Principle' which is a principle combining these four elements of what, how much and in what way you say things, in order to have a conversation.
Leech brought in a 'Politeness Principle' which defined politeness as forms of behaviour which allow us to co-exist in a harmonious manner. Therefore, his maxims are those of Tact, Generosity, Approbation, Modesty, Agreement and Sympathy. Conversation governed by these maxims are more polite and thus encourage harmonious co-existence.
To summarise: Grice talked about efficient and clear conversation, Leech was concerned with this, but also how the delivery of this conversation and how polite it is.
That is an incredibly over-simplified explanation but it might help in some small way.