Freeview Play is simply Freeview with extra goodies; those goodies being the catch up TV delivered by the internet. All they have done is package it in a way that's convenient and relevant to the Freeview channel offering, and that's why it offers just BBC iPlayer, ITV Hub, All4 and Demand5.
Smart TV features offer a broader range of services but often they're tethered to the TV manufacturer's idea of what
Smart TV should be. You'll probably find Netflix, Amazon Prime and Youtube along with a bunch of apps and services that feel more like filler content than anything relevant or useful. If you've been used to doing catch-up via a laptop or tablet then a Smart TV can feel like a backwards step because the interface is clunky and you can't go off reservation to add your own apps. You're also relying on the TV manufacturer to support those apps for the life of the TV; but as we have found, that isn't happening. Fortunately
Smart features are now integral to all but the most basic TVs so there's no price premium (or choice even) of 'with' or 'without'.
If you don't need to change the TV other than for this idea of adding Smart features then there's plenty of choice of plug-in boxes which will
Smartify your existing telly either to the same level or beyond. The
Now TV boxes are advertised on TV and their service range is pretty simple to understand. Basic catch-up TV is £6.99 per month. You can add Sky movies catch-up service for an extra tenner a month.
Amazon Fire TV and Google Chromecast are popular too.
Apple users have Apple TV as an option. This used to be heavily focused on a lot of US-only accessible content but that's changed. They integrated Now TV in to their product. The rest centers heavily on pay-to-view content from Apple Movies. However, these boxes do provide Apples screen mirroring facility 'Airplay' so what's on your phone can be seen on your TV. This works for things such as Sky's On Demand service for example.
Less well publicised and teetering on the dark side are the range of Android TV boxes. These provide access to vanilla services such as BBC iPlayer but also provide a platform for adding lots of other apps to access a 'broader variety of services'

if you get my drift. If you have your own video/music/movies library stored on PC or network drive then you should have a look at an app called Kodi. It's a media player but so much more besides.
IMO there's no single solution that ticks every box. The chances are that if your needs are quite basic then a Smart TV with Freeview Play might cover everything you want for now. I think there's still some upheaval due because the BBC are struggling to find a model that works for their digital content now that the Government have put the thumbscrews on them financially. They're handcuffed to the license fee in a time when linear TV is seen as less relevant to the younger generations. They can't fund online streaming via advertising so it wouldn't surprise me to see iPlayer become chargeable if consumed in a household without a TV license.