Matching attributes based on features' locations

[ScarlettDinh]

How do I match up the attribute table of these two shapefiles without either having a mutual field or having the shapes truncated through using the Cut tool? I want the address of the "test_parcel" to match into the "BF3". Another way to word the question is how do I match up the attributes based on the locations of the features? If there is a better group to ask this question please let me know, this is my first time asking. Thank you all in advance.

[DanaNolan]

Read up on Spatial Join. Spatial Join—Help | ArcGIS Desktop 

This can add the parcel number data to your other table, if that is what you want. The tool is part of the ArcMap Join tool although you do have to choose to join spatially, as join by attribute is the default. There is also a geoprocessing tool that does this, and will give you more options.