For me, algebra connotes the solving of a system of equations, such as 3x+9=y and 2y-5=7... I guess that the question marks or letters are some "pre-algebra" thing so that kids are used to seeing that form of problem before algebra? I've also heard about "differential equations" in seventh grade math, but it has not referred to solving a system of equations with more than one derivative present.
As for calculus, the way I learned it as "independent-study math" was that it dealt with analyzing the behavior of functions and families of functions (limits, derivatives, integrals, sequences and series...).
