Question: For the speed of a transverse wave in a string we use the formula

$$v= \sqrt{\frac Tμ } $$

and sometimes we use the formula $v =λf$. Are these two same or different?

Answer: 
They give the same value for speed, however, they are different; they relate the speed to different parameters.

The first relates the speed to the tension and the linear density, which gives the value of the speed in relation to the specific parameters of the string. Similar to relating speed of sound to temperature.

The second equation is a universal equation that relates to any type of wave. Simply, wavelength is the length of the repeating cycle of the wave. Frequency is how many cycles pass per second. This gives,

(length(m) / cycle) \* (cycles / second) = length passing per second = speed (m/s)
They are different, and both are true.

$v=f\lambda$ applies to all waves: strings, sound, water, light, every sort of wave (maybe not crime waves :-).

$v=\sqrt{T/\mu}$ is specific to transverse waves of strings. Waves in other situations have equivalent formulae coming from their specific dynamics.