I finally decided to search for the big spider on the internet, and it turned out to be quite easy as the species is very common.. and.. it also turned out that the small one and the big one I found around the house are the same species just different age (they actually grow a lot!).
These spiders belong to the 'Black and Yellow Garden Spiders' and they are very common around the world.
And.. I also found a website with Black and Yellow Garden Spider pictures that look very similar to the ones in our front yard. The owner of this website, David Cummins, doesn't have a 'contact me' button on his website, therefore I couldn't ask for his permission for putting a link. However, he has a 'tell a friend' button so, I hope putting a link on my blog here qualifies as telling a friend.
I am still a little afraid of spiders (I will tell you about it another time) but these garden spiders are very beautiful in the sunlight that I just love watching them.