Actually it depends on the order of the words: For instance, if I say "That is also true" or "That also is true" I am saying that two (or more) things are all true --- "That is true in addition to those other things". And if I say "That too is true", I am saying pretty much the same thing. However, if I say "That is too true", I am saying it is 'very' true, not that it is also true. So it seems that 'tambien' means 'too' in the sense of 'in addition to' rather than 'very' in English - but I am just learning so "No estoy seguro"
Correct means there is no error, it is accurate. True refers to factual veracity.
Wow, I never understood why non-native speakers struggled with that until I tried to explain it! I've always wondered why people say, “My sentence is true" when they mean “My sentence is correct." Now I get it! It seems so obvious if you understand it, but how does one clarify this better?
There are three forms of that (ese esa and eso), although only two forms of those (esos and esas). If you are clearly talking about an object, then you will always use the one which matches the gender of the object. The female form is predictable. It is esa revista or esa mesa. The male form, however, is not eso, but rather ese. So it is ese periódico or ese coche. You use the correct gender whenever it is clear, whether or not the object is mentioned by name in the sentence. But there are some times when you say that where it is amorphous and doesn't tie into an object. This is the "neuter" that, and eso is used. This is used in sentences like Eso es lo que pienso (That is what I think) or Eso es importante (That is important) The "eso" here does not tie back to an object with a gender, so the neuter version is used. But the plural of both ese and eso is esos, which brings it back to more of the norm as it is seldom that there is this same amorphous those as you do that. Eso is used perhaps a little more often on Duo because of the fact there is no context to the sentence. It is sometimes not clear without context whether some context would provide a gender. But Duo does tend to avoid those sentences which must have a gender but the gender is not specified. For example, Esa no es roja, es rosa. For this example I made it feminine because I was thinking camisa. But whatever it is that has a color, would also have grammatical gender. If it were a pink car, you would use ese. In this example it wouldn't make sense to say that there wasn't an object to tie it back to.
All this applies to este, esta, and esto as well.
Eso is the neuter that. It is used on cases like this where it doesn't refer back to a specific, gendered noun. Tal means such. In a few cases it might be translated as that, but such would also generally work. It does not vary by gender, only number.
Cierto means true or certain. It does not really mean correct, although they are closely related. I think the other example you were thinking of was where cierto was translated as right. True/false and right/wrong are synonymous in some circumstances,but I didn't love that translation. But if you goal is to understand what you read and hear, if you limit your translation to true or certain, you are less likely to misunderstand. Those translations will tell you to what extent correct can be attributed to the situation. Normally correcto is correct.