UNF = Unified Fine

UNJF = Fine series with controlled root radius - the external threads of the UNJ family have a tightly controlled root radius, the size of which depends upon the pitch of the thread.  They're widely used in aerospace components, as one example.  The internal threads have an increased minor diameter but not a controlled root radius, so a standard tap can be used.

My data shows 1/4-32 UNEF (extra fine) and 1/4-32 UNJEF - but nothing for 1 1/4-32, which sounds like a special thread of some type.

Thanks for your answer! Can you please tell me what type of class thread I should use. The drawing I'm doing calls for internal threading.

I really don't have enough info about your project to help you.  I've written a freeware program with lots of thread data.  Maybe that and a good reference book will give you what you need.

In general though, a medium-fit unified internal thread would be class 2B - a close fit would be class 3B

As an example, a threaded hole that would accept a quarter inch bolt with twenty threads per inch would be defined on a blueprint as:

1/4-20UNC-2B  or 1/4-20UNC-3B

you would also need to specify a thread depth


UNJ threads are normally class 3B


The program is at:
http://bellsouthpwp.net/r/s/rsnmar/METhreads.zip

dinkylink-
mrainer is right that the UNJ thread series is used in the aircraft industry.  This series is better in vibration and shock than the UN series.  

Look in Machinery's Handbook.  It has all Unified Standard threads.  A 1 1/4-32UNF sounds kinda weird.  Are you sure that's what is needed: a 1.250-32UNF thread?  Note that a UNJF-3A can fit in a UNJF-3B or UNF-3B but a UNF-3A can't fit in a UNJF-3B.

Lastly, note that drafting standards prefer the thread callout to be:  .250-32UNF-2A rather than 1/4-20UNF-2A.

Tunalover

Look in the Machinery's handbook. They have lots of thread information.