When looking at a fitting and trying to decide if a thread sealer should be used, you need to look at where the 'seal' on the fitting is located.
1) If there is a mechanical seal on the fitting, like an O-ring or washer, then no additional sealer is required.
2) If there is a flare or inverted-flare on the fitting, like an AN or brake line, then no additional sealer is required.
3) If the threads of the fitting are designed to do the sealing, then you should use Teflon tape or paste.
In the fittings that you have pictured, the one on the left looks like it has an O-ring on the end. No tape needed.
In the fitting on the right, it looks like there is an inverted flare on the end. Again, no tape needed.
Rule of thumb:
A pipe-thread (tapered thread) fitting will always require a thread sealer.
A straight-thread fitting will not require a thread sealer.
As with all rules of thumb, there will be exceptions. I have seen aftermarket fuel pumps that were provided with pipe-thread barb fittings that said in the instructions to not put sealer on the threads. I followed the instructions and the fittings didn't leak!
(Fuel pump manufactures worry that a piece of Teflon tape will tear off a fitting and get ingested by the pump)
I'm not sure if I helped but there you go!