Is the longitude assigned to sunspots spherical or projected? Sunspot maps are created from a projection of the sun, so the coordinates of sunspots (or active regions in general) are assigned according to it. 

Do these coordinates correspond to actual spherical positions, or are they altered as a result of the projection? 

Edit: After seeing the answer, I realized that a part of what I am asking about was not clear in the initial question. So here it is: Are the values of the sunspot coordinates as provided officially in spherical positions or in projection? 

A commonly used instance of "official" records is X-ray measurements from the NOAA GOES. The text files are found here. 

For example, see file for 2000. The output is documented here, under "Output File Specification".
The transformation from projected geometry to heliographic coordinates is straightforward.
As Peter Meadows explains, this can be done either mathematically, or graphically using a latitude/longitude grid template.
Since the solar equator is inclined about 7&deg; to the ecliptic, different Stonyhurst disks are used at different times of year.

W T Thompson 2006 section 2 describes the two main heliographic coordinate systems.
Latitude in both systems is measured from the solar equator.
The central meridian of longitude in Stonyhurst coordinates is fixed facing the Earth.
The Carrington coordinate system rotates rigidly with a sidereal period of 25.38 days, approximating solar rotation at a typical sunspot latitude of &plusmn;26&deg;.

The NOAA Space Weather Prediction Center's daily Solar Region Summary provides spherical coordinates in both forms.
Here are excerpts of two reports four days apart:

SRS Number 129 Issued at 0030Z on 09 May 2019
Report compiled from data received at SWO on 08 May
I.  Regions with Sunspots.  Locations Valid at 08/2400Z 
Nmbr Location  Lo  Area  Z   LL   NN Mag Type
2740 N08E14   307  0160 Cao  04   03 Beta
2741 N05E52   269  0160 Hsx  03   01 Alpha

SRS Number 133 Issued at 0030Z on 13 May 2019
Report compiled from data received at SWO on 12 May
I.  Regions with Sunspots.  Locations Valid at 12/2400Z 
Nmbr Location  Lo  Area  Z   LL   NN Mag Type
2740 N08W40   308  0070 Hax  03   02 Alpha
2741 N06W02   270  0210 Hsx  03   02 Alpha


According to their README,
Location is a latitude and longitude relative to the central meridian, and Lo is a Carrington longitude.
A typical sunspot region moves about 13&deg;/day from east to west in Stonyhurst longitude and less than &plusmn;1&deg;/day in Carrington longitude.

GOES X-ray event report columns 29-34 also appear to be Stonyhurst spherical coordinates.
For example, sunspot region 9042 was associated with several X-ray events in June 2000.
If you filter the report by that region number, you can see that its progress from E90 to W90 longitude is roughly linear in time.
In projection, the plot of east-west position vs. time would be sinusoidal, flattening at the limbs.