What is similar about why congress and the courts informally change the constitution? How do their methods changing the constitution vary?

Informal methods are used more than formal because formally amending the constitution requires achieving the popular vote, which is difficult task to achieve.

Once the bill has passed both houses, it goes to the states.

The other method is for the Constitutional Convention to be called by two-thirds of the legislatures of the states, and for that Convention to propose one or more amendments.

It is found in the fifth article of the U. S. Constituition. The similary lies to the fact that both ways demand a two third vote so that an amendment can be proposed, also the approval of an amendment depends on 3/4 of the total votes in either way.

The difference lies on how togather the votes: Congress itself - - either houses - - - or the courts formed by currently 34 states.