# What is it called when two problems are similar?

Suppose that there are two problems $P$ and $Q$.

How can I say that "solving $P$ is same thing with solving $Q$"?

For instance, if $P$ is NP-Hard, then we can say "$P$ can be solved in polynomial time iff there exists an algorithm $A$ that solves $Q$ in polynomial time".

There should be a shorter term for this, and I'm sure that is not similar.

Is equivalent the right word?

In complexity theory we prefer, when possible, to use formal definitions. Two problems $P,Q$ are polynomially equivalent if there are polytime functions $f,g$ such that $x \in P$ iff $f(x) \in Q$ and $y \in Q$ iff $g(x) \in P$. This is the usual notion of equivalence in complexity theory.
Sometimes we prefer a coarser notion of equivalence which allows using a problem as an oracle. Two problems $Q,R$ are polynomially equivalent with respect to oracle reductions if $Q \in \mathsf{P}^R$ and $R \in \mathsf{P}^Q$, or in other words, $Q$ can be solved in polynomial time with oracle access to $R$, and $R$ can be solved in polynomial time with oracle access to $Q$. Under this notion, 3SAT and co-3SAT (its complement) are equivalent.