What on earth is the difference between Calculus and Analysis [duplicate]

Calculus refers to a field of mathematics, originally created by Newton and Leibnitz, independently. When studying calculus, you normally start with single variable Calculus, then move toward multivariable calculus. The next part is Real analysis, which is the study of the theory behind Calculus.

Calculus is Analysis without proofs.

"Mathematical analysis" can refer to real analysis, complex analysis, functional analysis, abstract analysis, etc. Calculus (especially when being used as a word today) refers to the single/multivariable Leibniz/Newtonian calculus taught in high school and first year university courses for science/social science majors, which is split up into differential calculus (studying functions that are differentiable and that can be approximated by linear functions) and integral calculus (functions that are integrable) on $\mathbb{R}^n$.

Functional analysis considers analysis on infinite dimensional metric spaces, which is unintuitively much different than analysis on finite dimensional spaces.