Apple has filed a complaint against Swatch in a Swiss court over the use of the phrase Tick Different in a marketing campaign.
Swatch is using the slogan to market a wristwatch containing a contactless payment chip.
Apple says the phrase unfairly references its Think Different campaign, which ran in the 1990s.
According to Swiss news site Watson, Swatch chief executive Nick Hayek said the similarity was purely coincidental.
He said the slogan was a nod to one of its own campaigns from the 1980s: "Always different, always new."
Apple used Think Different in its adverts from 1997 to 2002, in what was thought to be a response to IBM's Think ad campaign.
A 1998 television advert, featuring black-and-white images of historical figures such as Einstein and Gandhi, won an Emmy.
In the complaint to the Swiss Federal Administrative Court, Apple's lawyers Lenz & Staehelin said the tagline was long considered "the core of the Apple brand".
Legal experts say that, to win the case, Apple must show that Swatch's use of the phrase Tick Different provokes an association with Apple products in the minds of at least 50% of consumers.
A similar complaint lodged at the same time with the Swiss Federal Institute of Intellectual Property was rejected.
Swatch was granted trademark status for the phrase Tick Different in the US in 2015. It also has the trademark for the slogan in Switzerland.
This is not the first time the two companies have clashed.
In September last year, the UK Intellectual Property Office upheld Swatch's opposition to Apple's efforts to trademark "iWatch" in the UK.
It ruled that the term was too close to "iSwatch" and "Swatch".