Copper pipes commonly use solder to join pieces together. As noted by others, up until the 1980's the solder was a 50/50 mix of tin and lead. I still have some old 50/50 solder in my basement. Eventually the solder transitioned to lead free, which is 95 percent tin, 5 percent antimony, which is the current copper pipe solder sold.
Galvanized pipe is typically joined by threading, there is no solder used, so if you have galvanized pipe in your house, you will not leach lead out. You will definitely leach zinc out, since the steel pipe is coated with zinc (the galvanization metal).
The Flint River water did not test positive for lead, that was never the issue. The issue is that the Flint River water is more corrosive to pipes than the Lake Huron water that Flint used to purchase from Detroit. The additional corrosivity of the Flint River water leached lead out of City of Flint lead water supply pipes, and perhaps leached lead out of the solder joints in houses that used copper pipe for water supply (probably most of the houses in Flint).
As a note, many municipalities have lead water supply pipes, and continue to use them. I worked on several Boston water supply project, and Boston still has some in use lead pipes, and some wooden ones as well. It is very expensive to replace water pipes, and of course infrastructure is chronically underfunded, so municipalities try to stretch the life of pipes to the end.