Overview: The difference between search logics when filtering by tags vs profile fields. One will yield in "AND" results while the other gives you "OR" results. Profile fields require that all criteria is met, while tags require that only one filter needs to fit.
Profile Fields vs. Tags: How to make the choice
One difference between tags and profile fields is in how they work when filtering.
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Profile Fields use "AND" logic; individuals have to meet all the criteria or it will not included in the output
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Tags use "OR" logic; individuals need to be in at least one of the tags selected to be including in the output
A closer look at profile fields and "AND" logic
Filtering for people using profile fields under People > Show More Filter Options uses "AND" logic.
In other words, it is looking for where all the criteria are true at the same time (the intersection of all the data).
The easiest way to visualize this is with a Venn Diagram:
In this illustration, the blue region is the area that would be included by "AND" logic. It contains Profile Field 1 AND Profile Field 2.
Here's a more practical example in Breeze terms:
In this search, we are looking for people who are male AND members AND married. They have to be all three to be included.
Again, the blue is what you will get in the output.
As another example, let's try this advanced search:
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First name: Ashley
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Birthday: In September
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Anniversary: In October
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Deceased: 12/25/0037
Doing this search would bring up only people named Ashley who were born in September, got married in October, and died on Christmas in A.D. 37. Likely a relatively small group.
A closer look at tags and "OR" logic
Any time that you select multiple tags, you are using "OR" logic. This means that it can be in one tag OR the other tag. It can also be in both.
This applies to:
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People > Show More Filter Options > Filtering by tags.
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Under role permissions, People > Only Access Certain People > People In Tags
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Any other place you use multiple tags.
You can also visualize this with a Venn diagram:
In this example, your search will return everyone in Tag 1 OR Tag 2 OR Tag 3. Notice that people are included whether they are in the intersection or not. Anybody that's not in any one of the tags will not show up in the output, illustrated by the white space around the tags.
Here's a more practical example in Breeze terms:
The output for this search will show anyone who is in the Biking Group OR John's Group OR Mom's Group.
A person only needs to be in one or more of the tags to be included in the output.
Thus, the output will include anyone who is in at least one of the tags. The Unwashed Masses will be left out.
Honorable mention
Filtering across multiple profile fields will result in an "AND" search, while filtering within a single profile field will result in an "OR" search.
Example:
I want to know everyone who is either the Head of Household OR Spouse. Because they are in the same profile field, checking both boxes will give me the "OR" logic.
Putting it all together
If you filter for Male, Member, Married, Tags: Bacon Study Group, John's Group, Mom's Group, you will only get males who are both members and married who are in the Bacon Study Group OR John's Group OR Mom's Group.
Record Visibility Perspective:
Use TAGS to easily see groups of people
Use PROFILE FIELDS to record information about a person
Permissions Perspective
Use TAGS when hiding that group of people to some users will be important (visitors, inactive people, etc)
Use PROFILE FIELDS when hiding a specific piece of information is important
Additional Notes to Groups Management
TAGS are best for static groups. A set list of people who participate.
PROFILE FIELDS are best for dynamic groups of all eligible people within a set of distinctions (all females, ages 18-25, who are single)