It looks like we have hints for both interpretations, that they mean (sometimes?) the same and (sometimes?) something different.
On one hand, we have quotes hinting that they mean something different (AN 5.151 vs DN 19):
AN 5.151: one should be ekaggacitta while listening to a Dhamma talk (so not alone):
suṇanto saddhammaṃ … avikkhittacitto dhammaṃ suṇāti ekaggacitto yoniso ca manasi karoti.
while listening to the good Dhamma … one listens to the Dhamma with an
undistracted and one-pointed mind; one attends to it appropriately.
DN 19 suggests something like singleness (being alone) for ekodi:
‘ekodibhūto’ti ahaṃ bhoto ājānāmi. idhekacco vivittaṃ senāsanaṃ
bhajati araññaṃ rukkhamūlaṃ pabbataṃ kandaraṃ giriguhaṃ susānaṃ
vanapatthaṃ abbhokāsaṃ palālapuñjaṃ, iti ekodibhūto’ti ahaṃ bhoto
I understand “Alone, intent”. That means that one goes off on one’s
own and chooses a lodging in the forest, at the foot of a tree, in a
mountain glen, in a rocky cave, a charnel-ground, in the jungle or on a
heap of grass in the open. This is how I understand “Alone, intent”.
But at the same time, ekodibhava, ekaggata and samadhi also seem to be sometimes equivalent:
We often have the sentence “labhati samadhi, labhati citassekaggata” so it seems that samadhi = citassekaggata
But then there is AN 3.101 and the like:
So hoti samādhi na ceva santo na ca paṇīto nappaṭippassaddhaladdho na ekodibhāvādhigato sasaṅkhāraniggayhavāritagato. Hoti so, bhikkhave, samayo yaṃ taṃ cittaṃ ajjhattaṃyeva santiṭṭhati sannisīdati ekodi hoti samādhiyati. So hoti samādhi santo paṇīto paṭippassaddhiladdho ekodibhāvādhigato na sasaṅkhāraniggayhavāritagato.
So samadhi can be qualified by ekodi or not, suggesting two layers of samadhi, one relatively superficial, the other more serious. Either citassekaggata refers only to ekodibhāvādhigato samādhi (and then ekagga=ekodi) or it may refer to various states that can be with or without “ekodi” (and then they are different).
And then we have the Chinese parallels that weigh in on the side of equivalence in meaning.
Quite a mixed bag here.