What's best calling these things depends on:

- Who is using the system;
- what is the nature of the action really being performed;
- what other actions may be performed.

# The Programmers View

With relation to databases (and data-driven APIs) there's the famous **CRUD** operations, which stand for **Create/Read/Update/Destroy** (and respectively **Post/Get/Put/Delete**).

In many programming languages you may first **create** a record, then **add** it to a container, then **remove** it from the container, then **destroy** or **delete** it.

Also, in programming, **change** often denotes something that is yet to be persisted (saved to the database or file), while **update** denotes persisting the change. **Modify** is not common, but you do get *modified records* as a flag for a non-persisted state (aka, *dirty records*).

# Everyday Language

You can argue that people will agree on these definitions:

 - You **create** something from scratch. Like create a new report.
 - Once in existence, you **add** something to a container. Like adding a person to the managers group.

 - By **modifying** something you change its properties. Like modifying a design.
 - By **updating** something you change the data, but not the design. Like updating someone's phone number.
 - By **changing** something you replace one existing thing with another. Like changing your profile photo.

 - By **removing** something you take it out of a container. Like removing something from the fridge - the thing still exist.
 - By **destroying** something you do the opposite from creating - gone forever. Like destroying a toy.
 - By **deleting** something you wipe it off, so it is no longer retrievable. This is said with the obvious exception that nowadays people are accustomed to the 'undelete' feature. So somewhat of an ambiguity here, but it is a standard in interfaces to use the term for permanent delation.

# My Recommendations

 - Prefer **Add** over **Create** unless there's a clear create-then-add mechanism. Although technically (and as you said) create means it never existed before, while programmers think about 'records' users think about the abstraction these stand for. While for you adding a person's record makes perfect sense, 'creating a person' or 'creating a task' is less intuitive than 'adding a person' (to the system) or 'adding a task' (to the task list). Obviously, if your users are IT professionals and fluent with what a database and records are, prefer create over add.
 - If persistance is involved, prefer **update** over change. Having said that, users are accustomed to 'save changes'. Don't use **modify**.
 - Prefer **Remove** for non-permanent removal, and **Delete** for permanent removal.