When I use the same menu type item in k2 component in joomla 3.3, the menu Home and
Πάμε ταξιδάκια menu items shows the same articles although the categories are different. Only when I change from k2 to joomla categories the menu works. Please help me pametaxidaki.gr/

Does this happen when the cache is turned off?

Krikor, thank you very much. After I turned off the cache everything turned to normal.

Nice to hear that.
You must make sure that the cache plugin is rendering last in the plugins order.

Also you may leave your menu module uncached.