Just bought a second tv for exactly this! And did a lot of research!
Smart = internet accessible (eg Netflix, YouTube, Prime)
Free view Play = itv hub, 4 OD, etc
FreeSat = some satellite channels and BBCiplayer but not the other catch ups
Free view HD = regular channels, some satellites, and some channels in HD (I can't tell the difference)
If you want to be able to watch all mainstream channels on catch-up, and Netflix, you need a Smart Freeview Play tv
From research, I think that the only brands that have both are Samsung and Sharp. But look at the specs very carefully.
I have a Sharp 32" smart FV Play for £160 from Robert Dyas online (through Ryman's) The same price Sharp tv from Tesco and Richer Sounds was not a smart TV.