I'm not an expert on IRT but my understanding is that the graded response model estimates the probability of endorsing a category compared to all the 'lower' categories whereas the partial credit model estimates the probability of endorsing a category compared to the adjacent 'lower' category.

Jonathan Templin and the group at the Psychometrics Centre have produced the following that may be helpful

Best wishes, Mark

https://jonathantemplin.com/files/irt/irt07abim/irt07abim_lecture03.pdf

https://www.psychometrics.cam.ac.uk/uploads/documents/catr/catr-workshop-session-4

Stata IRT Manual says (I put pcm in the comparison too):

grm fits graded response models (GRMs) to ordinal items. In the GRM, items vary in their difficulty and discrimination. This model is an extension of the 2PL model to ordered categorical items. The model gives one discrimination parameter and three difficulty parameters:

Discrim

Diff

>=1

>=2

=3

pcm fits partial credit models (PCMs) to ordinal items. In the PCM, items vary in their difficulty but share the same discrimination parameter.

The model gives one discrimination parameter and three difficulty parameters:

Discrim

Diff

2 vs 1

3 vs 2

4 vs 3

gpcm fits generalized partial credit models (GPCMs) to ordinal items. In the GPCM, items vary in their difficulty and discrimination. The model gives one discrimination parameter and three difficulty parameters:

Discrim

Diff

2 vs 1

3 vs 2

4 vs 3

In more general terms than the previsous answer: the (original) Rasch model for dichotomous items is a one parameter model (parameter is item difficulty). The Partial credit model (PCM; Masters 1982) is a generalisation of the Rasch model extending it to ordered categorical/ordinal items, and also a one parameter model. The graded response model is a two parameter IRT model (parameters are item difficulty and discrimination) for ordinal items, and thus an extension of a two parameter model for dichotomous items.

cheers

Tine