Superscripts, subscripts and fractions are formatted differently. Open an example in Overleaf  Setting mathematical styleThe maths styles can be set explicitly. For instance, if you want an in-line mathematical element to display as a equation-like element put \displaystyle before that element. There are some more maths style-related commands that change the size of the text.
Note that math mode ignores whitespace, in fact, this whole code could have been put on one line and still would have compiled correctly. Another thing to notice is the effect of the \displaystyle command. This command forces LaTeX to give an equation the full height it needs to display as if it were on its own line.
I think there are two separate aspects to your question. How does one control the size of integral, sum and product symbols?. How does one control the placement of the limits of integration, summation, and multiplication: side-set vs. below/above?. These two aspects can be addressed separately. To control the size of the operators explicitly, one writes either \textstyle for small symbols or.