Is ammonium chloride the same thing as ammonia, and do you need to use
the same caution in not using it with product that contain bleach? If,
for example,on the outside of my dishwasher there was slight residue
of a dishwasher detergent that contained bleach, then I later cleaned
the outside of the dishwasher with a product containing ammonium
chloride, would there be any negative reaction? Just trying to learn
safety, thanks.

It's generally best not to mix cleaning products. In this specific
case, there's a definitive statement from an authoritative source.
According to the Chlorine Institute, you should NOT mix household
bleach (sodium hypochlorite or NaOCl) with ammonium chloride (NH4Cl),
or with other ammonia compounds.

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"Sodium Hypochlorite Incompatibility Chart

Do NOT mix Sodium Hypochlorite (bleach) with ANY other chemical unless
adequate engineering controls and personal protective equipment (PPE)
are in place. Accidental mixing may cause dangerous conditions that
could result in injury to personnel and/or damage to property or the
environment.

 Incompatible Material               

 Chemicals and Cleaning Compounds containing ammonia such as...

- Ammonium Hydroxide
- Ammonium Chloride
- Ammonium Silicofluoride
- Ammonium Sulfate
- Quaternary Ammonium Salts (Quats)

 Mixing May Result In...

- Formation of explosive compounds
- Release of chlorine or other noxious gases."

The Chlorine Institute: Sodium Hypochlorite Incompatibility Chart
http://www.cl2.com/whats_new/NaOClCompatChart.pdf

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"SODIUM HYPOCHLORITE SOLUTION...

 Supplemental Health/Safety Data          
 CAUTION-DO NOT MIX WITH AMMONIA COMPOUNDS-
 CREATES GAS WHICH IS BOTH TOXIC AND EXPLOSIVE"

Material Safety Data Sheet
http://www.setonresourcecenter.com/msds/docs/wcd00020/wcd02054.htm

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"When bleach is mixed with ammonia-containing compounds,
monochloramine (NH2Cl) and dichloramine (NHCl2) are formed, which may
produce tearing, respiratory tract irritation, and nausea. These
compounds decompose in water to hypochlorous acid and free ammonia
gas; the former combines with moisture forming hydrochloric acid and
toxic nascent oxygen; the latter is a respiratory and mucous membrane
irritant and can cause pulmonary edema and pneumonia."

Center for Disease Control and Prevention: Epidemiologic Notes and
Reports Chlorine Gas Toxicity from Mixture of Bleach with Other
Cleaning Products
http://www.cdc.gov/epo/mmwr/preview/mmwrhtml/00015111.htm

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Google Web Search: "sodium hypochlorite" + "ammonium chloride"
://www.google.com/search?hl=en&ie=UTF-8&q=%22sodium+hypochlorite%22+%22ammonium+chloride%22
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I hope this is helpful. If anything is unclear or incomplete, or if a
link doesn't work for you, please request clarification; I'll be glad
to offer further assistance before you rate my answer.

Best regards,
pinkfreud