What is the difference between "Catechism" and "Canon Law" in Catholicism?

They are two separate books, and the English translations of the Catechism and the Code of Canon Law¹ can be found on the Vatican website. (The Catechism can also be found, in Flash format only, on the website of the US Conference of Catholic Bishops.)

A catechism is "a summary of religious doctrine", according to Merriam-Webster, and this is precisely what the Catechism of the Catholic Church (often referred to as the CCC) is. According to its Paragraph 11 (the points of doctrine in the Catechism are arranged by paragraphs),

This catechism aims at presenting an organic synthesis of the essential and fundamental contents of Catholic doctrine, as regards both faith and morals, in the light of the Second Vatican Council and the whole of the Church's Tradition. Its principal sources are the Sacred Scriptures, the Fathers of the Church, the liturgy, and the Church's Magisterium. It is intended to serve "as a point of reference for the catechisms or compendia that are composed in the various countries".

In other words, there are many catechisms (for example, the youth-oriented catechism YouCat) which can be used for teaching different audiences about the Catholic Church, but this is the source catechism on which all of them will be based. This is the second such "source catechism" (technically known as a "universal catechism") which the Church has produced; the first was the Roman Catechism or Catechism of Trent, produced shortly after the Council of Trent. The current catechism is closely based on this one; see my answer to a related question.

The Code of Canon Law, on the other hand, is specifically meant for Catholics, and more particularly for Catholics of the Latin Church. It is sometimes abbreviated as the CIC, an abbreviation of its Latin title, Codex Iuris Canonici. There is an analogous document, the Codex Canonum Ecclesiarum Orientalium or Code of Canons of the Eastern Churches, applying to the other sui juris churches of the Catholic Church. It is available on the Vatican website, in Latin only.

The CIC is a body of regulations, often described as "the oldest continuously functioning legal system in the Western world" (see the web page of prominent canon lawyer Dr. Edward Peters). It is the set of laws governing the behavior of Catholics (lay and ordained) in the Church.

As one might expect with a book of legal codes, there's a lot of nitpicky, very dry stuff in the Code; discussions of when and where particular laws will apply, what it means to say that a legal rule is in effect for a certain number of days, and so on. But there's a lot of very important rules on, for example, how the Sacraments need to be celebrated (for example, there are a lot of questions on this website concerning Catholic marriage, almost all of which refer to the very complex and clearly set out rules concerning marriage).

The CIC quotes the Catechism, and vice versa (I believe); the canons concerning behavior of Catholics are ultimately all based on Catholic theology, and especially in the discussions of the Sacraments there are routinely theological statements which are used as an introduction to the laws themselves. But the two are separate documents, with separate purposes.

¹ Note: There have been several changes to canon law which postdate the appearance of the Code on the Vatican website. The website's version of the Code has not been updated to reflect these. They largely reflect a rejection (based in practical experience) of a way for someone to formally declare themselves not part of the Catholic Church, and several updates to the process of gaining a decree of nullity for a marriage.

The Catechism of the Catholic Church is a book, promulgated in 1992 by Pope St. John Paul II, which seeks to explain the doctrine (that is, the body of teachings) that the Catholic Church holds. It was envisioned as a document which the faithful can turn to if they are in doubt whether the Church teaches something, and whether Catholics must therefore believe it, as well.

It was preceded by the Roman Catechism, compiled under the urging of the Ecumenical Council of Trent, in order to clarify the Church's teachings in light of the Protestant Reformation. The Roman Catechism, itself, was preceded by several smaller Catechisms, generally geared towards teaching the faith to uncatechized peoples like Amerinds and South/Southeast Asians.

The Code of Canon Law, on the other hand, is — as its name suggests — a code of laws, which are binding on Catholics. As you can expect, the Catholic Church is a large organisation, and it requires for its proper ordinance to establish a number of rules and bylaws, which discipline (among other things) how Sacraments are dispensed, how Religious should act, what are the powers of Bishops' Conferences, and other such matters.

The most recent edition of the Code of Canon Law was promulgated in 1983, also by St. John Paul II, superseding the first and previous Code, the compilation of which started under the pontificate of Benedict XV and ended under the pontificate of Pius XI in 1917 (and therefore is known as the Pio-Benedictine Code).

In essence, if you ask a question starting with "Do Catholics believe in...", you will probably find the answer in the Catechism. If you ask a question starting with "Are Catholics allowed/forced/forbidden to ..." or "What happens if Catholics disobey ...", then the answer is probably in the Code of Canon Law.