That is mostly true, in most situations when there are more buy orders than sell orders (higher buy volume orders than sell volume orders), the price will generally move upwards and vice versa, when there are more sell orders than buy orders (higher sell volume orders than buy volume orders), the price will generally move downwards. Note that this does not always happen, but usually it does.
You are also correct that for a trade to take place a buyer has to be matched with a seller (or the buy volume matched with the sell volume). But not all orders get executed as trades.
Say there are 50 buy orders in the order book with a total volume of 100,000 shares and the highest buy order is currently at $10.00. On the other side there are only 10 sell orders in the order book with total volume of 10,000 shares and the lowest sell order is currently $10.05.
At the moment there won't be a trade unless a new buyer or seller enters the market to match the opposing side, or an existing order gets amended upper or lower to match the opposing side. With more demand than supply in the order books what will be the most likely direction that this stock moves in? Most likely the price will move upwards.
If a new buyer sees the price moving higher and then looks at the market depth, they would most likely place an order closer to the lowest sell order than the current highest buy order, say $10.01, to be first in line in case a market sell order is placed on the market. As new buy orders enter the market it drives the price higher and higher until the buy orders dry up.