Is there any relation between "genius" and "ingenious"?

They seem to mean the same thing, yet when spoken they sound like the negative of each other.
What's the secret behind those two words?

On the surface, one might think that ingenious is somehow based on the word genius. Interestingly, this is not true.

The word ingenious does not actually have the in- prefix for negation. Instead, it comes originally from the Latin ingeniōsus, which means "intellectual, talented, ingenious". At times in history it was also spelled "engenious". Indeed, ingeniōsus appears to be the same root that gave us the word engine.

Genius was originally different, but evolved to have a meaning that is similar to ingenious. It came to us from Latin, but it was originally Greek. According to the OED, it mainly had the meaning of, approximately, "genie" or similar type of spirit, in Latin. Figuratively, it was also used to mean "characteristic disposition; inclination; bent, turn or temper of mind." In English, German, and most of the Romance languages aside from Latin, it had the meaning of "natural ability" starting around the 1600s. The OED speculates that the meaning of genie was pushed towards the meaning of ingenious because of "confusion" between the two (that is, their superficial similarity).

Though in view of the answer above, I thought to quote two answers from this Reddit question which retrograde to Proto-Indo-European. I edit them lightly to improve readability.

By: user 'gnorrn', 2015 July 26

The duality goes all the way back to Latin:

• genius meant "the tutelar deity of a person or place"
• ingenium meant "innate or natural quality, nature"

Both words ultimately derive from the Proto-Indo-European root *ǵenh₁-
("to produce, to beget, to give birth"). The prefix in- has several meanings in Latin. Here it does not have the privative/negation meaning (cognate with English "un-"), but the meaning of "in, into".

By: user 'wurrukatte', 2015 July 26

[Originally, the querier exemplified with 1. in cantation and in carceration and 2. in genius .]

In 1 and 2, in- is not the same prefix. It is the same morpheme for two different prefixes that happened to become homophonous.
In 1, in- means "not". This in- goes back to PIE '*n̥-', which gave Germanic languages like English the prefix 'un-'.
In 2, the other prefix in- is actually a preverb going back to PIE *h₁en, "in, into", which gave Germanic *in > English 'in', "in, within".

In Latin, both PIE forms resulted in the form 'in(-)'. In other languages, they didn't necessarily become homophones, just as in English, like Ancient Greek 'a(n)-' and 'en-'.

English also has two homophonous prefixes that mean different things: 'un-' meaning 'not', as said, goes back to PIE '*n̥-'.

In contrast, 'un-' can also mean "reversal , opposite" as used with verbs like 'undo', 'unlike'. This goes back to Old English 'an(d)-', from Proto-Germanic *and-, from PIE *h₂enti-.
This 'un-' is cognate with Ancient Greek 'anti-' and Latin 'ante'.