Most digital cameras include the shooting mode, the metering mode, and even the focus mode in the EXIF information. The EXIF information can be viewed with most photo processing applications such as Adobe Lightroom or the software that came with the camera. Not all applications will display every field of the EXIF data, so you may need to try more than one. If you need a free application that can open a variety of file formats and displays a fairly comprehensive list of EXIF information, give Irfanview a try.
Here's a screen grab from the EXIF information for a photo I recently took with a Canon 7D as viewed using Canon's Digital Photo Professional that is included with Canon DSLRs.
Below is the same information from the same photo when displayed using Irfanview. Notice that the focus information is in the 'Maker Note' section, which is a place for manufacturers to include non-standardized information in the EXIF info. This means it can and does vary from manufacturer to manufacturer how or even if the information is included. Adobe products tend to ignore most parts of the 'Maker Note' section of the EXIF data. Observe that Irfanview properly identified the focus mode as AI Focus, but failed to properly describe other fields in the 'Maker Note' section such as the sharpness setting indicated by Canon's code '-32769' or the ISO value indicated by a '32767' code. In the standardized section of the EXIF not visible in this screen grab, the ISO used is properly identified as ISO 2500.