Is it true that when bid volume is more than ask volume the price tends to move down and when bid volume is more than ask volume the price tends to move up?

Your two statements seems to be the same 'bid vol ask vol', not sure if it is an error but I will try my best to provide my own insights.

It is hard to determine price direction based on bid/ask volumes, if you are primarily just looking at current price. Some volume may be heavily skewed to one side, e.g. most bid volumes may be placed below the current price of the stock, meaning people are expecting the stock to come down. (Stock trading at $100, bulk of bid volume are limit orders at $90).

Bid/Ask volume can certainly display some sentiments within the market. If Bid Ask, you may infer it as there are more buy orders as compared to sell orders. When it is Ask Bid, then maybe there are more sellers in the market.

However! This way of infering volume is very artifical as people with leveraged accounts can place this orders and cancel it anytime they want. Fun fact, the 2010 stock market flash crash was caused by huge orders which ended up being cancelled - this caused an artifical bump in demand for the stock, misleading high frequency trading computers and market makers into selling the stock.

Hope that helps.