Adobe Reader is the software which is to read and view pdf files, fill pdf forms, print pdf files, email pdfs
Adobe Acrobat is used to do everything which the Reader does and Which the Reader does not do. Acrobat is used to create pdfs, create forms, edit pdfs, modify them, print them and much more which the Reader cant do.
Check out Adobe.com to know more about both softwares.
On one hand, Adobe Reader is the free software which you can download from Adobe.com and use lifetime.
Acrobat is a paid software which is free to use as a trial for only one month. You can download the same from Adobe.com too.