I recently overheard a conversation where Adobe Acrobat Pro was referred to as simply “Adobe” and was understood. This was not the first time I’ve heard this. For the record PDF is a semi-open standard that can be viewed by a variety of programs including the program that comes with Mac OS and iPhone OS called Preview. Occasionally a PDF can contain some extensions that render it useless to these other programs and require that the user must have Adobe Acrobat Reader to view and use the document. These can be referred to as Acrobat PDFs. Those are the rare case and should be shunned.
Adobe has created an expectation that the only way to view an PDF is with their product. Additionally if you want to edit a PDF you need their Pro product. Neither is explicitly true, especially on the Mac OS. There are a number of free or lower-cost alternatives like PDF Pen from Smile on My Mac. Smile on My Mac has a nice comparison chart of PDF features.