Your basic terms are fine, and most users should understand them, but for consistency sake I'd make them more similar - there's a subtle inconsistency that could make them slightly... Not ambiguous, but just slightly slower to comprehend. Namely, you miss on word from each description
I'd prefer something more like the following:
- Upload new file
- Attach existing file
Or if there's a header such as "Select file" then it could be
- Upload new
- Attach existing
I prefer the latter, and would suggest using 'Option buttons' to make it clear that there'a a choice between two mutually exclusive action.
The only downside to 'Attach existing' is that it could cause a little confusion in terms of, for example, a photo - 'upload new' could sound like you take a new photo and attach it, while 'attach existing' could be uploading a photo from your phones library
An to 'attach existing (file)' could include the following, which makes it slightly more obvious
- Attach previously uploaded
- Select from previously uploaded
- Attach from server
- Select from (website name)'s library
- Attach from your (website name) library
I quite like the first and last, personally