The differences between recurrences

i’m not sure that im fully understand which recurrece is asymptoticly big tete (n) and which is big teta of (log(n)). im asking becuse in lecture 15 , about adders, guy mentions that the delay of comp - adder is big teta (log(n)) and the recurrence looks like the recurrence of big teta (n).
can you define the differences between the two ?

dan levy

I dont understant the question.
use O(n), \Omega(n), \Theta(n) to improve readability

what i mean is that the diffrence between a recurrence that represents a growth of Θ(n) and a recurrence that represents a growth of Θ(log (n)) is unclear to me. if you can show an exemple / format of each function it would be helpful.

f(n)=1+f(n-1) solves to f(n)=\Theta(n).
g(n)=1+g(n/2) solves to g(n)=\Theta(\log n).