From the following definitions and examples, it is apparent that the two words are the same and that all that distinguishes them is the extra 't'. The version that is now spelled with two 't's, tends to be of English cuisine, and the single 't' of French heritage.
I suspect that at a restaurant, you would pay twice as much for potage compared to pottage.
There is further room for confusion as English spelling did not standardise until the 18th century and is still not complete (compare wagon and waggon).
Pot[t]age: In both cases, they indicate a soup/stew that borders on a paste - pottage more so; potage less so.
OED pottage, n.
Etymology: < Anglo-Norman and Old French, Middle French potage,
I. A soup, stew, or porridge.
1.a. A thick soup or stew, typically made from vegetables, pulses, meat, etc., boiled in water until soft, and usually seasoned. Cf.
potage n.
Now chiefly archaic or historical, but occasionally applied to regional dishes.
?c1225 (▸?a1200) Ancrene Riwle (Cleo. C.vi) (1972) 301 Hwase is
ouerfeble. Potage eoteð bliðeliche. [whoever is feverish [will] eat
pottage without a problem]
1682 G. Wheler Journey into Greece i. 43 Christmas pies,
Plum-potage, Cake and Puddings.
1973 C. A. Wilson Food & Drink in Brit. vi. 206 ‘Bukkenade’ was
another meat pottage for veal, kid, hen or coney. It was seasoned with
herbs and spices, thickened with egg yolks, and sometimes sharpened
with a little verjuice or vinegar.
2. Oatmeal porridge. Now rare (Scottish in later use).
a1500 (▸1422) J. Yonge tr. Secreta Secret. (Rawl.) (1898) 244
(MED) A man Sholde ette mettis of colde and moisti
complexcion..as..Potage of oot-mell.
2015 D. Kynoch in Lallans 86 19 His bowel o pottitch steed Far it
haed been sin brakfast, nivver aeten.
potage, n.
Etymology: < Middle French, French potage (see pottage n.)
Soup, esp. a thick soup typically made from vegetables, meat, etc. Cf. pottage n.**
In modern use generally denoting a soup of French origin or character.
1653 I. D. G. tr. F. P. de la Varenne French Cook 274 Potage of
Brocolis, they are the young sprouts of Coleworts.
1938 Life 6 June 10/3 (caption) Place a thick crusty slice of
toast in each petite marmite. Pour the rich, savory-smelling potage
over the toast and sprinkle with plenty of grated cheese.
1998 N. Lawson How to Eat (1999) 235 The grainy potage produced
by the split peas is wonderfully satisfying.*