Note that we have a separate page that explains what is an acid and a base
This is a subject which confuses many chemistry students. They are accidentally confusing the specific scientific term "strong acid" with the thought that it means it is a concentrated acid or a corrosive acid. But in fact it means neither of these things.
A strong acid is an acid which is fully ionised in solution.
This also means it has a very large value for the equilibrium constant for the ionisation reaction. Strong acids are so fully ionised in solution (close to 100%, but not quite) that the equilibrium constant has values much greater than one million.
e.g. HCl(aq) + H2O(l) H3O+(aq) + Cl-(aq) Greater than 99.99% ionised
There aren't very many strong acids, which makes life very easy for you. It is possible to memorise all the strong acids, so that you then know that anything other than these ones are automatically weak acids.
A weak acid is an acid which is only partially ionised in solution. This also means that it has a small value for the equilibrium constant for the ionisation reaction. The value tends to be less than one, and quite a lot less than one.
e.g. CH3COOH(aq) + H2O(l) H3O+(aq) + CH3COO-(aq) Less than 0.4% ionised.
Anything at all that is not in the strong acid list must be a weak acid. Easy, isn't it. So now you can tell instantly if something is a strong or weak acid.
By some strange coincidence, there are no medium acids - they either ionise a huge amount or not very much at all.
Notice at no point did we say a strong acid was a concentrated solution - a solution of one gram of sulphuric acid in ten litres of water is a solution of a strong acid. The word strong refers to the acid's ability to ionise, not the concentration of the solution - it is a weak solution, or more scientifically, a dilute solution.
Nor does strong acid refer to it's corrosiveness. The above solution is not very corrosive at all - you could stick your hand in it until you were bored to death, but it wouldn't do you any harm. But sulphuric acid is a strong acid. Interestingly, pure sulphuric acid is not ionised, so by definition the liquid is a weak acid, but it is very concentrated and very corrosive indeed. Hydrofluoric acid, HF, is a weak acid and is extremely corrosive indeed - it eats glass, and has to be stored in plastic containers.
Similarly, a strong base is one which is fully ionised in solution.
It also has a high value for the equilibrium constant for ionisation.
Again there are not many of them, and again you can memorise them all.
Again, anything else is automatically a weak base.
As before, this means that they have a small value for the equilibrium constant for ionisation.
Again, there is no reference to the concentration of the solution, or how corrosive it is.
Note that contrary to what most people imagine, bases are much more dangerous than acids. I have accidentally been splashed in the eye by acids a few times when the drops got over the top of the safety glasses I was wearing. Luckily it wasn't concentrated acid, and I managed to quickly wash it away with no problem and no pain. But get a solution of a base in your eye and you are in real trouble. It will be extremely painful and you will probably go blind if not treated immediately. Bases react with the cornea of the eye and eat it away. Very nasty. Even very dilute solutions do this. So be very careful when handling these substances. Never pour them into something above eye-level and always wear eye protection.
Ever wondered why bottles of sodium hydroxide solution usually have a plastic stopper instead of the glass stopper you get with bottles of acids? Sodium hydroxide can dissolve glass a tiny bit. Get some on the stopper, it dissolves the glass a tiny bit, then the water evaporates, and the stopper becomes extremely hard to remove as the two glass surfaces join together. Still think bases are not as dangerous as acids?
Now you should look at the section on the general definitions of acids and bases