TRICHOCEREUS.

Whenever I think 'Echinopsis' I think of common globular clumping cactus..
How is a T.bridgesii, peruvianus or pasacana like that?

On thinking about it, I'd even go one step further and bring back Lobivia in addition to Trichocereus and Echinopsis. I think that there are enough differences between these three to justify it.

Don't Lobivia spp. flower during the day time?
and accordingly have bright-coloured flowers in order to attract their diurnal pollinators like bees?

In contrast to the true Echinopsis spp. (at least the wild type original species) which have white or pale nocturnal flowers in complementary order to attract their pollinators (moths?)

That's a small distinction right off even if it's not much buts its all I got.
I agree, I think that there are differences, but not being an expert in these or any cacti in general I cannot really speculate further. definitely a physical difference also.

I believe the two can cross fairly easily?
how about Lobivia x Trichocereus?

FWIW
When it all comes down to it,
you can call a plant whatever you wish.
bestowing plants which have existed
for however many thousands of years
before their discovery
with scientific names
in accordance with the artificial system of
Linnaean taxonomy
with binary nomenclature
is never going to be 100% effective.
Enthusiasts indulge in detailed debates,
often with a near religious fervour,
about the technicalities of where a said plant ought to be classified,
perhaps they should just worry about growing them.
just my 2c.

Someone once told me, collectors like to separate the groups and see what makes their plants different for each other. Biologists like to to group them and see what they have in common.

Naturally, I like using Trichocereus.

FWIW
When it all comes down to it,
you can call a plant whatever you wish.
bestowing plants which have existed
for however many thousands of years
before their discovery
with scientific names
in accordance with the artificial system of
Linnaean taxonomy
with binary nomenclature
is never going to be 100% effective.
Enthusiasts indulge in detailed debates,
often with a near religious fervour,
about the technicalities of where a said plant ought to be classified,
perhaps they should just worry about growing them.
just my 2c.

I like this. Personally I think taxonomy is an acknowledgement of the level of difference plants have from each other. To me I think it's important.
Then again maybe I'm one of those religious enthusiasts...

Can I use the name soehrensia? I like that name.

I use Trichocereus for my columnar plants, where as i use Echinopsis for my globular clumping plants.