OTC stocks and their foreign stock exchange equivalent

Do OTC stocks trade similarly to their foreign exchange equivalents?

I’m looking at a company that is not available for US investors on the ASX, but it has ticker on the OTCQX. My broker shows me historical data for this ticker, and it shows it never rose above $0.6 all the way back to 2002; whereas if I look at other charting sites, it shows historical price data similar to the ASX component.

I’m not sure who to believe. I would have thought that the OTC equivalent trades just like it would on its primary exchange, with the only difference in price being the currency used.

Do OTC stocks not trade at the same value as their foreign exchange component?

Edit: the company is ASX:DYL and OTCMKTS:DYLLF; charts:

• OTC: DYLLF (screenshot)
• Fidelity: DYLLF (screenshot)
• Google: DYL (screenshot)
• Google: DYLLF (screenshot)

I’m just unsure why OTC/Fidelity show such low pricing for the OTC stock in years when the company is trading for much 4-5x on its primary exchange duirng that time; plus I’m not sure why Google/StockTwits/Tradingview/SeekingAlpha all show similar price history for the OTC stock but OTC/Fidelity don’t. OTC says that DYLLF has been a member of OTCQX since 2018, so perhaps that is where the discrepancy occurs and the charts from Google are showing the history of the primary exchange ticker (DYL)?