I do not have a copy of Photoshop Elements installed currently,
however, the effect you are looking for is quite simple.
Each part of the image is compiled on a seperate layer - lets look at
your first image as an example. There are three main layers:
Layer 1: The white background
Layer 2: The red filled logo outline.
Layer 3: The white logo elements.
Layer 1 has no effects and nothing by the white background.
Layer 2 is transparent with only the red logo element, and has two
layer effects applied: A black 'outer glow' and an 'inside bevel'.
Layer 3 has the same two effects, only the transparency on the 'outer
glow' is much less, so that the shadow effect is less prominent.
The second image is compiled in a very similar way, only the layer
effect used on the logo layer is called a 'pillow emboss'.
You should ba able to alter the layer effect settings to produce
different levels of shine on your image.
A simple guide to using the Photoshop Elements layer effects can be
By using the technique demonstrated in that link on text layers and
layers with transparent areas, you should be able to create effects
that are very similar to those demostrated in the images you provided.
In searching for details on the implementation of these features in
Photoshop Elements, I also came upon the following site, which has a
good range of Elements tutorials.
As for a similar effect in Illustrator, that is unlikely. I have no
used Illustrator in a number of versions, however the fact that
Illustrator is working exclusively in vector graphics makes effects
like this pretty much impossible, however Photoshop images and layers
can be imported into Illustrator documents, although it restricts, to
some extent, the flexability offered with vector graphics.
I hope this helps, I am a little blind to the specifics of the
Elements version of Photoshop, however I have been using various
versions of Photoshop for many years. Let me know if you have any
problems, or if my explanations are unclear.