Second’s pendulum:
It is a pendulum that takes precisely one second to move from one extreme position to other. Thus, its time period is precisely 2 seconds.

Simple pendulum:
A point mass is suspended by an inextensible, massless string from a rigid point support. In practice a small heavy spherical bob of high-density material of radius r, much smaller than the length of the suspension, is suspended by a light, flexible, and strong string/thread supported at the other end firmly with a clamp stand.

The distance L between the point of suspension and the centre of spherical bob (centre of gravity), is called the effective length.
L = l + r + e

where, l is the length of the string from the top of the bob to the hook,
e is the length of the hook
r is the radius of the bob.

The simple pendulum executes Simple Harmonic Motion (SHM) as the acceleration of the pendulum bob is directly proportional to its displacement from the mean position and is always directed towards it.

The time period (T) of a simple pendulum for oscillations of small amplitude, is given by the relation,

where, L is the effective length of the pendulum

g is the acceleration due to gravity