Are all #2 live centers compatible with a lathe #2?

Both the Oneway and Woodtek are very good as far as I know.
I have the Nova and it is 2MT.
The Miniature Extension is good if you are wanting the tailstock back for the work more.
The Threaded Center and the Hollow Cup & Point are also 2MT which means you can use them in the headstock. The Hollow Cup & Point as a "Safety Center" and the Threaded Center with your customization as a drive center.
The Nova is also three sets of bearings instead of two.
http://www.tools-plus.com/nova-lathes-5015.html

I may be wrong but I believe the Oneway and the Woodteck can also be used in the headstock when you lock it with a pin. But then what do you do for a live center in the tailstock? Buy another?
Using the Threaded Center in the headstock the rest of the live center can be used in the tailstock with the Nova.

The OW and the WT can be used with custom centers but you have to drill and tap for the 3/4 X10.
With the Nova I use tee nuts. Drill for the tee nut shaft and drive it in. In the future is steel against steel.

This shows the Threaded Center in the headstock used as a friction drive. The smaller rubber ball in the second pic is just right for candle sticks, etc.


Just some of the centers.

I screwed up by mentioning the live center in my chuck thread and this conversation is now fragmented.

@Lee, started watching the Pearce video. Thank you, it's PERFECT for me. I'll have to finish later as I have to head out to treat my golfing withdrawals.

I believe that what came with my lathe is indeed the "dead cup center" or safety center, as seen at 16:00.

@The Dane recommends the Wodtek center, which is similar in appearance to the Oneway that I had mentioned. What confuses me is all the discussion about $10 centers, when I'm considering a $120 center. Makes me think either we're not talking about the same thing or I'm about to waste my money on something that I don't need.

I do like that Steb center because all I have are 2 and 4 drive spurs. I love the idea of being able to stop the piece, especially because my #90 have the big crank lever, which is not ideal for frequent starts/stops.

Terminology can get confusing as to centers.
Others may well disagree with me and that is fine.

A Dead Center is used in the tailstock and does not revolve (have bearings). This would be like the $4 center I posted a link to at ebay. This is an old style due to no bearings and turners would often add a bit of wax or oil to the tip to keep it from burning the wood as the wood rotated. The Dead Center is normally just a point, or a ring, or a cup & point. The Ring center is typically hollow to allow you to pass a drill bit through it such as in drilling for a lamp. The Cup & Point may or may not have a removable point.

A Live Center is used in the tailstock and varies in price due to quality and adaptability. It will have bearings (either 1, 2, or 3) and rotate with the work. Most new lathes come with a one bearing live center. Below is a link to the Nova standard equipment live center. I had a one bearing in my old jet and used it for 25 years with no problems at all. http://www.tools-plus.com/nova-lathes-2mtlc.html

A Drive Center is used in the headstock to of course, drive the work.
This may be a four-prong center, a two-prong center, or a steb center (these are the three most common).

To confuse things….. remember that Cup & Point from the tailstock? It can be moved to the headstock as a Drive Center. It does not bite into the wood like a prong or steb but relies on friction alone.
Adding more pressure from the tailstock increases the amount of drive.
I believe it was Alan Lacer who made it popular for folks starting out because if you had a catch the wood would stop spinning instead of coming off of the lathe. Since the wood stopped spinning Alan called it a Safety Center. I did buy a couple of the $4 ones and I do think it helped my daughter to not be as afraid of the lathe. I used mine a few times but once you learn the tools and how to not get a catch they are more of a pain than they are worth IMHO. A drawback is because it relies on pressure from the tailstock, a small diameter spindle may flex (bow) under the pressure. Seems to work well for tool handles or other stout work.

I know this is OT to your original question of Morse tapers but my use of terminology seems to differ from others.

Here is a MT chart but doesn't take into account mini, midi, or full size lathes. Anyone of centers listed should work well with PM 90.

http://www.drill-hq.com/2012/04/morse-taper-dimensions-chart/

Oneway live center
http://www.packardwoodworks.com/Merchant2/merchant.mvc?Screen=CTGY&Store_Code=packard&Category_Code=lathes-acc-cent-revtail-olc

Hold Fast
http://www.packardwoodworks.com/Merchant2/merchant.mvc?Screen=PROD&Store_Code=packard&Product_Code=110977&Category_Code=lathes-acc-cent-revtail-hflivcenad

Nova
http://www.packardwoodworks.com/Merchant2/merchant.mvc?Screen=CTGY&Store_Code=packard&Category_Code=lathes-acc-cent-revtail-nova

Live Center that came with my Jet called Oneway clone and which looks lot like Woodtek Center, Dane likes. Well still use my simple $30, G1293 from Grizzly bought over twenty years ago. Started using it on a Delta 700, Jet Mini, and now my Jet 1642. OEM center collects dust mostly. Still use a dead center for tuning pens when turning between centers although mount the dead center in the head

Goood luck with it!