The difference between hydroxide and oxyhydroxide I cant discern these two terminologies. Would someone be very kind to help me on it?

I think hydroxide mean M(OH)x where M is a metal ion, while oxyhydroxide means something like MO(OH). Is that right? Oxyhydroxide equals to oxide-hydroxide.
Yes, you have correct idea.

Oxyhydroxide is any mixed oxide and hydroxide. For example Iron(III) oxide-hydroxide

While in hydroxide hydrogen and oxygen atom are joined with covent cond.