They are not the same thing.
Induction is the process of proving a formula or theorem on the basis that , the theorem is true for one value of a variable, then proving that it is valid for the next value of the variable. Finally, it is proven that the theorem is valid for all values of the variable.
Usually there is only one variable (integer) on basis of which the proof by induction is based.
Reasoning is to prove a theorem, or law or principle, or to prove an equality by deriving step by step from the input to the final step. At each step, (arithmetic and logical) formulas, theorems and inequalities known are used to arrive at the target.
The reasoning is usually done for all values or a subset of values of a variable or multiple variables. There are one or more variable in most of reasoning exercises.