The installer for Acrobat PRO and STD DC is same. It is licensed to PRO or STD once you enter the corresponding serial number or Sign in using the Adobe ID with the corresponding subscriptions.
1) Serial number based licensing:
The serial number for Acrobat STD & PRO are different. Check if the correct serial number was used when installing and activating Acrobat.
2) Named User licensing:
Use the Adobe ID which is associated with the subscription to Acrobat DC.
Note: If you purchased an Acrobat DC subscription or Named User License, you need to download and install a separate Acrobat installer.