Since your question appears to relate to US stocks and daily data, I'll tailor my answer to that.
Open, High, Low, Close, Volume
Data from individual trades (time, price, volume, exchange, trade condition codes) and trade cancellations are aggregated to produce open, high, low, close and volume appropriate for whatever time period is shown (daily, 15 min etc.).
Different providers may use different interpretations of the exchange and trade condition codes to provide a different set of data. Some providers might even only report trades from a single exchange.
Consolidated Tape Association
In the US, the Consolidated Tape Association governs the rules about which trades, times and condition codes affect the Open, High, Low, Close and Volume. These rules are generally accepted as the standard method of reporting..
For example, the Open is the first regular trade reported across all trading venues after 09:30:00.000. The close is the primary listing exchange’s closing auction result, if there is an auction. If there is no auction it’s the last traded price reported to the tape (across all eligible venues).
Note that some types of trades are excluded in affecting the price (OHLC) such as odd-lot trades, average price trade, contingent trades etc. All trades affect the volume. Also consider the effect of busted/cancelled trades.
There are further exceptions to this rule. For example, in March 2018, the SEC approved a change to the official closing price for NYSE Arca securities that have derivatives (such as options) listed against them. If they didn’t have a closing price auction or had a closing price auction with less than a round lot, then the closing price will be compromised of both a time-weighted average price of the midpoint of the National Best Bid-Offer over the last 5 minutes of the trading day and any last-sale eligible trades during that period.
The rules are here: https://www.ctaplan.com/tech-specs
under CTS Binary Output Specifications
Adjustments for Corporate Actions
Historical data can be adjusted for various corporate events such as stock splits, spin-offs (de-mergers), stock dividends, special dividends, special distributions, capital distributions, normal dividends, distributions in a currency other than the trading currency, events that give the holder a choice of multiple options etc. There are often different interpretations for the surviving entity of spin-offs/de-mergers too, which can cause discrepancies.
Discrepancies between different providers are commonplace. Ask your provider exactly how they handle trades from multiple venues, how the open, high, close and volume are calculated, and if/how corporate actions are adjusted.
Disclosure - Norgate Data is a data vendor.