To be heading for something / somewhereTo be headed for something / somewhere
>> Ir rumo a algo / algum lugar.
_To be on one's way
You should read: Way
.I’m on my way home
>> Estou a caminho de casa
.'Cause I'm on my way to the ocean
>> Porque estou a caminho do oceano
In poetic literature, the expression to be one's way
is considered more detailed and sometimes deeper. If you are on your way, you have started your journey somewhere.
(1) Pearson Education. Longman Dictionary. 2004.
(2) Collins Online Dictionary.