If you enable the additional privacy lists in uBlock Origin and clear your Cookies frequently, then not really.
In fact, Firefox Focus is functionally equivalent to Firefox's Private Browsing. They both don't keep Cookies, browsing history and such, and they both have a tracking blocker with the same blocklist (sourced from disconnect.me). Most ads have trackers in them, which is why this tracking blocker also blocks most ads (neither of them have a dedicated ad blocker).
Where they differ is that Focus is obviously just not a full-featured browser - no browsing history, even if you want it, no bookmarks, no extensions, no sync, and tabs are still a bit awkward in it. It's also generally mostly intended for the kind of user that has trouble finding or understanding Private Browsing. It being in a separate app makes it accessible from a place they know, the app launcher, and it explains nicely that browsing history and such won't be shared, as data is generally not shared between separate apps.
On a technological level, the big difference is that Focus uses Android WebView (on Android; on iOS it uses WebKit) instead of Gecko as browser engine. This helps to keep the APK size really small, which is desireable, because you sort of expect users to install it as secondary browser in addition to their full-featured browser, and well, it wouldn't help Mozilla's market share that much anyways, if they'd put Gecko into it, since it blocks most ads (and users will probably use their full-featured browser for online shopping and such, too), therefore hardly generates revenue for webpage owners, therefore wouldn't really incentivize them to optimize for Gecko either.
Some advanced users like to have Focus around alongside a full-featured browser, because you can tell Android to open links in Focus by default, meaning all the random links that you might click on in other applications will open in it, not cluttering up your browsing history and not leaving behind cookies or just in general fingerprinting you further. And if you then do want to open a webpage in your main browser (maybe also just to save it into your browsing history), then Focus does have a convenient button for that.
In fact, Firefox Focus is functionally equivalent to Firefox's Private Browsing. They both don't keep Cookies, browsing history and such, and they both have a tracking blocker with the same blocklist (sourced from disconnect.me). Most ads have trackers in them, which is why this tracking blocker also blocks most ads (neither of them have a dedicated ad blocker).
Where they differ is that Focus is obviously just not a full-featured browser - no browsing history, even if you want it, no bookmarks, no extensions, no sync, and tabs are still a bit awkward in it. It's also generally mostly intended for the kind of user that has trouble finding or understanding Private Browsing. It being in a separate app makes it accessible from a place they know, the app launcher, and it explains nicely that browsing history and such won't be shared, as data is generally not shared between separate apps.
On a technological level, the big difference is that Focus uses Android WebView (on Android; on iOS it uses WebKit) instead of Gecko as browser engine. This helps to keep the APK size really small, which is desireable, because you sort of expect users to install it as secondary browser in addition to their full-featured browser, and well, it wouldn't help Mozilla's market share that much anyways, if they'd put Gecko into it, since it blocks most ads (and users will probably use their full-featured browser for online shopping and such, too), therefore hardly generates revenue for webpage owners, therefore wouldn't really incentivize them to optimize for Gecko either.
Some advanced users like to have Focus around alongside a full-featured browser, because you can tell Android to open links in Focus by default, meaning all the random links that you might click on in other applications will open in it, not cluttering up your browsing history and not leaving behind cookies or just in general fingerprinting you further. And if you then do want to open a webpage in your main browser (maybe also just to save it into your browsing history), then Focus does have a convenient button for that.