No. Blackheads and pimples are both forms of acne, but they are different kinds of breakouts. A blackhead (open comedo) forms when excess oil and dead skin cells clog a pore that stays open; the dark color comes from a reaction with oxygen in the air, not from dirt.
A pimple develops when a clogged pore becomes inflamed. Without pus it is called a papule; with pus it is a pustule. You can have blackheads and pimples at the same time, and dermatologists often recommend different over-the-counter ingredients depending on the breakout type.
Source: American Academy of Dermatology — Acne: Signs and symptoms