An omission of 'that is'

Nothing has been omitted.

These are merely sentences that use different structures to reach the same goal.  Think of it this way. I am traveling from City A to City B. There are several different highways between the cities. Each highway is different, but each reaches the same destination. Highway #1 does not leave out sights you would see on highway #2. Those sights just are not there -- and they never have been.

I have some money saved. -- highway #1 uses an object complement to modify "money"

I have some money that is saved. -- highway #2 uses a relative pronoun clause to modify "money"

Just different grammatical structures. Same result. Same meaning.

I hope this helps.

I have some money that is saved for my wedding. I have some money that is left to have dinner with you.

I have some money that is saved.  The underlined is an adjective clause because it describes a noun.

I have some money saved.  The underlined is an adjective phrase beginning with past participle.  Structure is different but they have same meaning.