The problems you have the same result because they are both DigitalVideo Broadcasting (DVB) systems. Both rely on being able to get perfect reception of digital bitstream. Single bit errors cause sound loss and pixilation or pictures to freeze. See the pictures on this page:
However, the transmission systems are different and the same outcome is caused by different problems.
The satellitesignal problem is normally caused by dish alignment problems, or can be caused by the path to the satellite being blocked. Realignment requires technical equipment and should be performed by an engineer.
Your Freeview problems are caused by insufficient signal being fed to the Freeview TV. Yes, you should check your cables and connectors are in very good order, but you may need a slightly better aerial.
Yes, the signal will increase in strength at switchover, but if your equipment is damaged you may still need a new aerial.