At issue are many factors. In broad strokes these include Intonation, String quality, Tuner Quality (Thanks @CarlWitthoft).
Intonation, in this context, is the fixed tuning of the instrument. This can be adjusted on electric guitars at the bridge. Guitar repair shops will do this setup on electric guitars for a price. Shops around me call it a "supertune". Some of what you pay for with more expensive acoustic guitars is good intonation. Some of the cheaper guitars lack this.
Symptoms: A guitar that has poor intonation has strings that when the open string is in tune, the octave at the 12th fret is out of tune. Actually the way most guitarists test this is to check the twelfth fret harmonic with the twelfth fret note, if they match then your intonation is at least OK. The way the guitar is constructed it is near impossible to have perfect intonation but on a good well setup guitar the imperfections will be slight.
Resolution: If you have an acoustic guitar, new strings might help (see strings). Otherwise it's time to get a better guitar. If you have an electric guitar then you can learn how to fix your intonation, but a guitar repair shop will do a professional job.
Most guitar strings available on the market will produce quality intonation on a quality guitar, but there are some stinkers out there. Make sure you have a good set of strings. Bad strings and dirty strings can produce poor intonation.
I assume that the strings are on the correct places on the guitar. If the strings are mixed up, or are the wrong type for your guitar it can also affect the intonation. There would be other problems such as string tension that is to tight or too loose that would make this an obvious issue however.
Dirt, patina, rust (usually black), etc. or bad intonation (see intonation).
Resolution: Replace the strings.
We can tell from your picture that your tuner in particular, while chromatic, does not tell you what octave you have tuned your string to. If you tuned to the wrong octave, your guitar would definitely sound weird if not out of tune. Also, as Carl is pointing out, your tuner may not be as picky as you would like it to be. At best, your tuner is difficult to use. While it does work and I could use it, if you gave it to me free of charge I would refuse it for being too difficult to use.
Buy a new tuner.
Note: @RockinCowboy and @Tetsujin are correct and worth a read, so I won't retread what they have said.