By Hari Parshad Das
Both terms are used synonymously.
For example, while performing parikramā of tulasī-devī, we call it a pradakṣiṇā — “tāni tāni praṇaśyanti pradakṣiṇaḥ pade pade”
Pradakṣiṇā means — To walk around completely (pra) while keeping the deity to the right (dakṣiṇa)
The Hari-bhakti-vilāsa (8.393) specifies the method for performing Parikramā/Pradakṣiṇā of any deity of the Lord:
bhaktyā bhagavato hareḥ
nāmāni kīrtayan śaktau
tāṁ ca sāṣṭāṅga-vandanām
Translation of Commentary: If one has the required strength then the same pradakṣiṇā should be performed with aṣṭāṅga-praṇāmas.
Definition of Aṣṭāṅga-praṇāma (from Hari-bhakti-vilāsa 8.162):
urasā śirasā dṛśā
manasā vacasā ceti
praṇāmo’ṣṭāṅga īritaḥ
Note of caution for ladies performing aṣṭāṅga-praṇāma (From the Skanda-purāṇa, Vāsudeva-māhātmya section, Chapter 29, Verse 27):
praṇāmaṁ puruṣas caret
pañcāṅgam eva nārī tu
nānyathā muni-sattama
Translation: The men may perform aṣṭāṅga or pañcāṅga praṇāmas (according to their capacity). However the women should perform pañcāṅga only and not otherwise.
Being non-judgmental about Govardhana-parikramā: Sometimes devotees think that barefoot parikramā of Govardhana is superior to wearing shoes, or that walking is superior to taking a vehicle. One should not consider one type of parikramā as superior to another. Srila Jiva Goswami says in the Gopāla-campū (Pūrva, 15):
svacchandatvād yānam apy atra diṣṭam
Translation: It is not required that the parikramā should be performed by foot. One can also take a vehicle (and obtain the same result).
sādhu-caraṇa-rajo ‘bhilāṣī,
hari pārṣada dāsa.
PS: I have not gone into a detailed etymology of the terms because I wanted to avoid grammatical complexities. Those who are interested in knowing the etymological derivations, please contact me personally.