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Evangelism is the act of telling someone about Jesus Christ, in the hope that they will convert to Christianity - i.e. that they will become believers in Jesus Christ.
A disciple is someone who is a follower - specifically someone who obeys and puts into practice the teaching of their master. Making a disciple involves teaching people - by education and example - to do what Jesus calls them to do. This is different from someone who is simply a believer. Although belief is a necessary first step to discipleship, someone who is just a believer may do so without putting his teaching into practice.
Most people and churches who evangelize do hope and expect that their converts will become disciples, and to that extent there is a large overlap. Most churches will do both at least to some extent, and the difference becomes a matter of emphasis.
In the extreme case, a church with a very heavy focus on evangelism can treat their new converts as having 'arrived' i.e. learned and done everything they need to do (with the possible exception of making other converts). All their resources are focussed on the unconverted, seeking to bring them to a point of belief. A church with a strong discipleship focus will teach and mentor new converts more, so that they learn more and follow Jesus better - such teaching continuing for the whole life of a Christian.