Lead generation is a method of acquiring new customers. Imagine it's like fishing — you use various baits to attract the attention of potential customers and get them interested in your products or services. In this context, both companies and private consumers are the fish you want to catch.
In this process, you give the potential customer (the Leads) the ability to voluntarily provide you with information about yourself, usually by filling out forms on your website, signing up for a newsletter, or downloading a free freebie. You then use this data to learn more about them and address their needs in a targeted manner.
Lead management is the overarching term for all the strategies and tools that you use to generate leads. It's like the entire fishing kit — the rod, the reel, the line and the various baits that you can use, either individually or in combination, to best catch your “fish.”