You summed up with your own words what we know here very well, but under a different naming convention.
Smoking with lips, like when you normally smoke a cigarette, is sintethised here as "MTL", i.e. "Mouth to Lung" - as you aspire smoke in your mouth, and then breathe it down the lungs.
Smoking within the chest, we define it "DTL" - i.e. 'Direct to Lung" - as you breath the smoke directly into the lungs.
You'll find the majority of cigarette smokers are MTL, as it is a behaviour induced by the limited airflow of a cigarette. I was a MTL smoker.
Vapers don't all DTL vape. The type of device defines your style. In a DTL device, the airflow is so wide that you can actually breathe thru the device.
MTL is normally characterised by small airflow, high strenght nic e-liquids and low power, while DTL is characterised by large airflow, low strenght nic e-liquids and high power.
While the nicotine intake between the two styles is possibly the same, the vapor production, the taste / flavour profile, and the general look of it all, are completely opposite. The choice of style is something you have to decide for yourself.
I do most of my vaping MTL style. Some of my vaping is DTL (Gangnam) style, mostly to taste new flavours or to blow some clouds (it is truly fun), or to test some new vaping gear.
When I smoked, it was all MTL.
DTL smoking was limited to some desperate moments of my life, or after a long abstinence - think after two back-to-back flights, amounting to 12 to 18 hours without smoking.