To complement what @gary_sc said:
An Illustrator file (if saved as PDF with "Preserve Illustrator Editing Capabilities" or even as Ai with a PDF preview) contains 2 streams of data sets. The PDF data set is used by programs like InDesign to display the Illustrator file. You can also use Acrobat to display the PDF part of an Ai file. That's what I give as a message, when sending someone an Ai file, who may need or want to look at that file, but who has no Ai.
What you edit in Acrobat is effectively only the PDF part of the file. Luckily, Acrobat seams to ignore the Illustrator data, so that saving your PDF file does not take away the possibility to edit in Ai. There is no guarantee, however, that third-party programs are also so kind or that all data is preserved.
So, golden rule: edit in the source program if needed and only when that is not possible, try Acrobat with a copy.
As a side note: you can also save your PDF file without the Illustrator part. In that case, you will get a standard PDF file, that cannot be edited any more in Ai.
Now, Ai can also open as one of its import formats PDF files, but you will see, that, if you do so, all the Illustrator context is gone. PDF files can be pretty messy for the human, as they are not intended to be edited by us. The ideal PDF file gets send to a printer or a display, without having anyone touching the data.