Candlesticks from kline API don't match candles from Binance.

When I get candlesticks for Futures Perpetual pair with REST API “GET /fapi/v1/continuousKlines”/“GET /fapi/v1/klines”, they don’t match the candles I see on Binance. Volume is different and all OHLC prices are different too. How can I get the exact candlesticks I see on Binance Futures pair?
Data from API (Time-OHLCV):
2022-04-21 03:35:00 265.66 267.09 265.58 266.75 5396.447
Data from Binance Futures:
2022-04-21 03:35:00 266.54 268.25 266.54 268.05 4727
These are 5m candlesticks and they are closed.
Another question:
When I try to get candlesticks for AAVEUSDT pair I get this:
Why do I get data like that for some pairs?
Thanks in advance!

thanks for the feedback, could you please help to give more details of how those data was fetched, it can help us to investigate.

These API GET requests in Python:
“GET /fapi/v1/klines”
“GET /fapi/v1/continuousKlines”
And then form a Pandas dataframe from the response I got.
By “Binance candlesticks” I mean candlesticks from Binance Futures site/TradingView.
Maybe I am doing something wrong? I need to get X amount of last candlesticks for Futures pair. I know I can get candlesticks via websocket, but thats not what I need. Maybe I need to use different requests or baseurl?

Are these details enough or should I share more? @dino

I have the same problem for LTCUSDT on testnet futures account. Is there any solution for this problem? I use python functionalities:
client.get_historical_klines(symbol, interval)