What does the suffix “-saurus” mean?

Solution 1:

The two etymologies are different.

In thesaurus, the -saurus isn’t a suffix. It’s part of the word. The word actually comes from the Greek word thēsaurós, which means treasure or treasury.

In tyrannosaurus, the origin is from the Greek words turannos, which means tyrant, plus the word sauros, which means lizard.

Solution 2:

They have different origins:

thesaurus ORIGIN late 16th cent.: via Latin from Greek thēsauros ‘storehouse, treasure.’ The original sense [dictionary or encyclopedia] was narrowed to the current meaning by the publication of Roget's Thesaurus of English Words and Phrases (1852).

tyrannosaurus ORIGIN modern Latin, from Greek turannos ‘tyrant’ + sauros ‘lizard,’ on the pattern of dinosaur.

From NOAD.

So, obviously, they do not have the same meanings. Although some people do like to make jokes about this. Cf. What's a big-vocabulary word for someone with a big vocabulary?

Solution 3:

According to Wikipedia, thesaurus derived from Latin and meant “treasure store”. So assuming the first half of the word is treasure, then saurus must mean store presumably.

Contrarily, tyrannosaurus derived from the roots tyrannos and sauros from Greek, which meant “tyrant lizard”.

Therefore, since one derives from Latin and the other from Greek, I would assume the similarities in the roots are purely coincidental.