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If you go to settings-apps-installed and tap on a particular app,don't you get several options from which you can move to sd card?
Yes,that option is for the devices with internal sd card,not external.I do not know then,I do not own Z1,so I cannot figure it out right now.Maybe someone else knows,wait for other answers.
I understand,maybe some just cannot be moved from phone memory.

Maybe your phone needs rooting in order to change those parameters.
If i not mistake...the apps can transfer to SD card option was removed after Jelly Bean version(Ice Cream Sandwich still available for that options)so for Jelly Bean version you can only move Media file like Video,Picture etc. to sd card only for apps is not available to move to sd card anymore....for 4.4 Kit Kat version not sure they will add in this option back or not still can't confirm unless developer to add in.As for Root maybe possible.
Yes,it could be how you say.Maybe it moves a lot faster with the apps in phone memory.