What is the difference between TISE and TDSE, physically , how to visualize it? I am asking that we are solving the se for time dependencies and independence but what does they mean actually what are we getting actually when we solve them?
 A: Time Dependent Schrodinger Equation (TDSE)
\begin{align}
\hat{H} \Psi(\mathbf{x}, t) = i\hbar \frac{\partial}{\partial t}\Psi(\mathbf{x}, t)
\end{align}
governs the dynamics of a general wavefunction $\Psi(\mathbf{x}, t)$ as time evolves. $\hat{H}$ is the Hamiltonian operator of the system.
Obtaining a closed form solution for $\Psi(\mathbf{x}, t)$ is generally difficult. Therefore, one would perform a series expansion on $\Psi(\mathbf{x}, t)$ as shown below
\begin{align}
\Psi(\mathbf{x}, t) = \sum_{n} c_{n} \psi_{n}(\mathbf{x}) \; e^{-i E_{n} t / \hbar}
\end{align}
where $c_{n}$ is determined by the initial condition (we shall intrepret its physical meaning later). 
What so special about $\psi_{n}(\mathbf{x})$ is that it is governed by the Time Independent Schrodinger Equation (TISE) given by
\begin{align}
\hat{H} \psi_{n}(\mathbf{x}) \; = \; E_{n} \,\psi_{n}(\mathbf{x})
\end{align}
where $\psi_{n}(\mathbf{x})$ is the energy eigen-state of $\hat{H}$ with eigen-energy $E_{n}$. Solving simple TISE, for example: particle in a box, is to solve a PDE with boundary conditions. It is the boundary conditions give rise to the discrete nature of eigen-energy $E_{n}$ (You can also have continuous energy spectrum for unbounded state. But we focus on bound state for simplicity)
Note that TISE is an eigenvalue equation. 
There are two physical interpretations for $\psi_{n}(\mathbf{x})$


*

*$|\psi_{n}(\mathbf{x})|^{2}$ as probability density of finding a particle at position $\mathbf{x}$ is time independent (known as stationary state)

*If the system is in the state of $\psi_{n}(\mathbf{x})$ and you measure the energy, it is given by $E_{n}$ with certainty


Since we have probability interpretation for wavefunctions, we demand the normalization conditions:
\begin{align}
\int_{\mathrm{all \; space}} |\psi_{n} (\mathbf{x})|^{2} \, d\mathbf{x} \; = \; 1 
\quad \mathrm{and} \quad 
\int_{\mathrm{all \; space}} |\Psi (\mathbf{x}, t)|^{2} \, d\mathbf{x} \; = \; 1
\end{align}
With these conditions, we can deduce that $\sum_{n} |c_{n}|^{2} = 1$. So $|c_{n}|^{2}$ also carry a probability interpretation and it goes like this: Suppose our general wavefunction is given by $\Psi(\mathbf{x}, t)$. When we perform energy measurement on  $\Psi(\mathbf{x}, t)$, there is a probability of $|c_{n}|^{2}$ to measure the energy as $E_{n}$, and the system would collapse to $\psi_{n}(\mathbf{x})$.
So, TDSE describes a general wavefunction $\Psi(\mathbf{x}, t)$ while TISE describes the energy eigen-states $\psi_{n}(\mathbf{x})$. Also,  $\Psi(\mathbf{x}, t)$ can be expressed as a linear combination of $\psi_{n}(\mathbf{x})$
To sum up, we usually tackle the problem as follow:


*

*Solve TISE to obtain $\psi_{n}(\mathbf{x})$ and $E_{n}$. Usually, involve solving a PDE with boundary conditions

*Form a linear combination of $\psi_{n}(\mathbf{x})$ to get a general form of $\Psi(\mathbf{x}, t)$

*Find the coefficient $c_{n}$ using the initial condition.


Hope this help :)
A: While other answers have correct information, they seem to primarily focus on the TISE and either it's "derivation" or how to use it. But all you are asking about is what do they mean and what do we get when we solve them.
I will answer the second question first. We essentially get the same thing when we solve them: the wave function of the system that evolves according to the SE. This is true of any differential equation. When we solve a differential equation, we are just finding the function (or functions) that make the equation true. An analogy is in solving the equation $x+2=3$. We want to find any $x$ values that make the equation true. Of course, we can say that solutions to the TISE have certain properties as others have pointed out, but at the end of the day we get the same thing either way, the wave function of the system.
As for what do they mean, they each describe how the wavefunction changes through space and time. This is also true of any differential equation. For example, with Newton's second law we have $F_{net}=ma=m\dot v$. So this equation tells us how the velocity changes over time based on the force and the mass of the object. The SE tells us how the wavefunction changes as well, but it changes over space and time, since derivatives with respect to both $x$ and $t$ are present.
With that being said, the wavefunctions always behave according to the TDSE. The point of the TISE is, like others have said, because for Hamiltonians that do not have time dependence, the wavefunctions that solve the TDSE have a form $\Psi(x,t)=\psi_x(x)\psi_t(t)$ (or more generally a sum of such terms), where $\psi_t(t)=e^{-iEt/\hbar}$, and $\psi_x(x)$ solves the TISE. You can get into the more specifics of how to solve these equations or what the wavefunctions themselves mean, but at the end of the day the answers to your two questions are what are true for any differential equation.
