See what I did there? Here are some common, yet often overlooked, examples of grammatical tautologies.
heir apparent
end result
general public
doctorate degree
undergraduate student
root cause
old adage
major breakthrough
close proximity
self-confessed
final outcome
There are lots of tautological proper nouns, like the Los Angeles Angels (The the angels angels: Spanish) or Lake Tahoe (Lake the Lake: Washo). But they just are what they are.
Pleonasm can be syntactic or semantic.
Semantic pleonasm occurs when the grammar of a language allows for a word or words to be be left out of a sentence without changing the meaning. “That” is a commonly semantically pleonastic word in English:
“I thought that you had read it” can be replaced by “I thought you had read it.”
Syntactic pleonasm is what we more commonly call a redundancy, such as this one taken from a popular book:
What therefore God hath joined together, let no man put asunder.