TL;DR Torsional strain can be thought as the repulsion due to electrostatice forces between electrons in adjacent MOs. Meanwhile steric strain (also known as van der Waals strain) can be thought as the repulsion when two bulky groups which are not directly bonded to each other become too close to each other and hence there isn't enough space for them.
Here is the more detailed version.
Torsional Strain
Lets consider an ethane molecule. The C-C sigma bond is free to rotate and in principle there are an infinite number of possible conformations. However only 2 are significant, these are staggered and eclipse conformations. Different conformers are usually drawn as Newman projections as they can easily be compared with each other. Below are the Newman projections for the eclipsed and staggered conformer:

The staggered conformer is the most stable conformer while the eclipsed conformer is the least stable conformer. The staggered conformer is approximately $\mathrm{12~kJ~mol^{-1}}$ more stable than the eclipsed conformer. This energy difference between this maxima and minima is known as the torsional barrier.
So what is torsional strain? The reason for the eclipse conformer being higher energy than any other conformers is due to the destabilising electrostatic repulsion between the electron pairs of the C-H sigma bonds on the two carbons. Furthermore, there also exists a stabilising feature which is greater in the staggered conformer. In the staggered conformer there is a constructive orbital interaction involving the bonding and anti-bonding MOs of the adjacent H atoms. This results in hyper conjugation which stabilises the compound.

The two effects that I have mentioned above is what torsional strain refer to. So you can think of torsional strain as the strain that is the result of electrostatic forces.
Steric Strain
Now lets consider butane. Rotation of the $\mathrm{C_2-C_3}$ sigma bond also lead to infinite possible conformers. However there are 4 main conformers shown below:

Here there are 2 types of eclipsed conformers which are the least stable of the conformers. The most unstable one is known as the eclipsed syn form. The syn form is approximately $\mathrm{20~kJ~mol^{-1}}$ higher in energy than the staggered conformer. The reason for this can partly be attributed to torsional strain as there is repulsion between the electrons in the sigma bonding orbitals. However also it can largely be attributed to the repulsion of the two relatively bulky methyl groups as they become too close to each other and there isn't enough space for them.
This repulsion is known as steric strain. Therefore steric strain can be define as the repulsion which occurs when non-bonded groups which are not directly bonded approach each other too closely. This repulsion only exists for bulky substituents, such as methyl or ethyl groups. So in ethane there is no steric hindrance as the hydrogen atoms are not that bulky.