The consonant sounds in "ship" and "measure" are both made by putting your teeth together, with your top teeth in from of your back teeth, and putting your tongue in the middle of your mouth, scrunched up towards the back of your mouth.
If we make these sounds the same way, then what is the difference between them? The difference is not what we do with our mouths, but what we do with our voice.
When we make a "sh" sound, we do not use our voice; the sound is quiet. Put your hand on your throat and make the sound in "ship". You should not feel any movement in your throat.
However, when we make a "zh" sound, we do use our voice. Put your hand on your throat and make the sound in "measure". Can you feel the vibrations?
There are not many words in English with the sound in "measure", and very few words with this sound at the beginning. This sound is mostly found in words that came into English from other languages in the middle or at the end of the word.
Want to practice more? Here's a handout to practice the sounds "s" and "sh."
The sounds in "ship" & "measure"