Here is the one with the transformer.

The switching modules in the first post do NOT have a transformer, that's a choke that is used in the switching power supply.  The second one with the transformer looks to be an isolated supply, but I'd have to see the description to be sure.

here is the description.

AC to DC Power Module Supply Isolation module Input AC90-240V Output 3.3V 500mA

Specification:
The power supply has a temperature protection, over-current protection and short circuit protection, AC90 ~ 240V wide voltage input, DC3.3V output, compact, 431 precision regulator.
1, Input characteristics
Input Voltage: AC90-240V 50/60HZ (full load)
2, Output characteristics
Output voltage: DC3.3V (±0.1V)
Output current: 0 - 500mA , MAX peak current :600MA
Output Power: 2W
Output efficiency: 85%
The output ripple: 150 mv
Size: 40*15*15mm
3, Reliability requirements
Environment 25 ° C under 80% load MTBF more than 100,000 hours

Package Include:
AC-DC Power Module Supply x 1

I'm pretty sure the "Isolation" module means the inputs are isolated from the outputs. 

Note that it requires 115 VAC input...

thanks ..i spaced on the ac input.

here are the specs on the first module pictured.

I have the first module pictured, that one is must certainly NOT isolated, and you should NOT ground either of the outputs to the input common or you'll get fireworks.

Obviously, the links to the actual modules would be very useful so I didn't have to go searching for them.

This is the non-isolated module, I use these.

From what I find on eBay for similar looking modules, this one is probably isolated.