In the USA, pink and rose are almost the same thing. Pink is the general category, and ROSE is just a more specific shade of pink. There is light pink, soft pink, deep pink (ROSE), etc.
Obsess is a verb that shows extreme "wanting" of something to a great extent. Sometimes when a person OBSESSES over an issue, it becomes bigger than what it really is. This issue becomes an OBSESSION.
example: The young girl OBSESSED about her upcoming test so much that she studied three hours every night.
CHASE is also a verb with the intent of going after something or someone. (abstract or concrete)
Example: The cat chased the mouse. The graduate chased his dream of becoming a doctor.
On a side note, sometimes this new generation will use these in a slang way. :) Let me give that to you too. (My teenagers do.)
Example: Mark obsessed after Sarah. (meaning....Mark IS OBSESSED with this girl.)
Example: Mark chases Sarah. (literally....Mark wants to date Sarah.)
***I hope that this helps!