The simple form is the same share, one isin, quoted on two venues; arbitrage keeps the currency-adjusted prices aligned. The harder form is a dual-listed company structure, where two separately incorporated parents share cash flows by contract while each keeps its own listing and shareholder register.
In the second form the two lines are not interchangeable, so a persistent price gap can and historically does open between them and can stay open for years, because no mechanism forces convergence.
Example: two legs of a dual-listed structure are contractually entitled to identical dividends. One trades at $54 and the other, converted at spot, at $49. The 9% gap is not arbitrageable because the shares cannot be exchanged.
Related: cross-listing, isin, sedol, adr, index-inclusion