Is it a difference in the tenses? Like one's a present and the other is future? Explain with examples please And can we say 什么也不 and 什么也没？
Let's begin with 什么都 meaning "everything"; see Expressing "everything" with "shenme dou" at the Chinese Grammar Wiki. We can add a verb or an adjective afterwards:
什么都 + adjective
which we negate with 不:
什么都不美丽 (everything is not beautiful)
什么都不辣 (everything is not spicy)
什么都不简单 (everything is not simple)
This is the easy case. See also the "Negating Adjectives" section of Standard negation with "bu".
什么都 + verb
which we negate with 不 or 没 or 没有, which is where it gets tricky.
At this point, it's no longer about 什么都, but only about 没 vs. 不. The most prominent Chinese.SE post about this is Why is 有 (yǒu) the only verb that requires 没 while other verbs can use 不?. See also the Chinese Grammar Wiki's article Comparing "bu" and "mei".
The following is a common construction; how it's usually taught. Given tsh's comment below, it looks like there are other constructions beyond this (which I'm unable to comment on).
什么都不 + verb vs. 什么都没 + verb
Indeed "没 + verb" often indicates a past non-event. From Negation of past actions with "meiyou":
Usually verbs can be negated with 不 (bù), but that construction is used for habitual or present actions. If the verb is about an action in the past, though, 没有 (méiyǒu) should be used.
So for example:
什么都没吃 = 什么都没有吃 (to not eat anything [in the past])
什么都不吃 (to not eat anything [present or future])
什么都没买 = 什么都没有买 (to not buy anything [in the past])
什么都不买 (to not buy anything [present or future])
Note that 没有 is an exception here, e.g. 明天什么都没有 (to not have anything tomorrow [future]) is okay. I believe 什么都没是 is also incorrect (there's a mismatch between 没 and 是).
(Please note, I'm just a learner. Hopefully if there's any misunderstandings on my part, someone can point them out to me in the comments.)
In general, 不 means "no" or "not" while 没 stands for 没有 and is closer to "don't" or "don't have". So 他什么都不吃 means something like "he does not eat anything", while 他什么都没吃 means "he didn't eat anything". So in this case, 不 conveys the meaning that something is universally not true (e.g. he is someone who just does not eat anything, or at least during a specified period of time he just does not want to eat anything) regardless of time or place, whereas 没 conveys the meaning that something did not happen/is not happening/will not happen specific to that time or place (e.g. he just happened to not eat anything on that day).
It's misleading to distinguish 不/没 by the "tense" it indicates. The information about time is always inferred form the whole context in Chinese.
Bold font is where the time information is mainly inferred from.
1.没 表 已然/不存在（没 indicates things that have already become a fact, which can also be a presumed fact/the state of non existence.）
他什么坏事都没干。（He hasn't done anything bad）
到时陈词庭上，你还要说什么坏事都没干？（By the time you argue in the court, will you still insist that you haven't done anything bad?）
大火过后，什么都没了。（After the conflagration, everything is gone.）
2.不 表 单纯否定/意愿（不 indicates simple negative/willingness.）
她逛街向来什么都不买。（She always buy nothing when shopping.）
她昨天逛街什么都不买，只看衣服。（Yesterday during the shopping, she didn't bought anything, but only chose clothes.）
什么都不干他事。（He had nothing to do with all the business.）
他什么都不做，对小组成绩毫无贡献。≈他什么都没做，对小组成绩毫无贡献。（He didn't do any work, so he contributed nothing to the team accomplishments.）（The former stresses more on subjective willingness.）
什么也不 indicate don't + anything/everything , 什么都没 indicates haven't / didn't + anything/everything.
我什么都没有 ， I don't have anything. 我什么都不要， I don't want anything.
我什么都没做， I didnt do anything, 我什么都不做， I don't want to do anything/ I won't do anything
One indicates the situation while another one indicates the intention,