Sir in trading chart of candle stick while opening we see gap up or down and in heikien ashi we see continuous candle what is the difference?

Explained very well on Stockcharts, check this link

Heikin-Ashi Candlesticks are an offshoot from Japanese candlesticks. Heikin-Ashi Candlesticks use the open-close data from the prior period and the open-high-low-close data from the current period to create a combo candlestick. The resulting candlestick filters out some noise in an effort to better capture the trend.