How does the Catholic Church differ from other denominations
such as Lutheran, Methodist and Baptist?

For the first thousand years AD, most Christians were one (Orthodox Christians are the exception). It is a sad truth of our history and our present reality that differences in theology, sacraments and church governance have deeply divided followers of Christ. The link below will highlight important differences.

However, in a spirit of Ecumenism, in today's multicultural and multi denominational communities, it is at times better to focus on the things that join us together. All Christians believe in one God, one faith, one baptism in Jesus. Groups such as the Franciscan Sisters and Friars of the Atonement (whose name is literally: at-one-ment) inspire us to work together for the good of one another, “that all may be one” one day. http://www.saintaquinas.com/christian_comparison.html

1. http://www.papalencyclicals.net/Pius12/P12MUNIF.HTM