Essentially, yes, the technique is the same for steeping and mashing.
The differences between mashing and steeping is in something you can't see- the enzyme activity going on.
The only difference between steeping and mashing is in the grain. If you use some base malt, that has enzymes available, the technique you described is "mashing".
If you use grains like crystal malt or chocolate malt, it's "steeping". Those malts have been pre-mashed, so to speak, so no enzyme activity will take place when you steep them.
If you use some base malt, it's mashing. If not, it's steeping. I hope that helps.
I used to use a mesh bag to line my bottling bucket, and did partial mashes in there. You can save money by buying some grain instead of all the extract in the recipe.