There have indeed been some confusion among the word heregeld and Danegeld as an Old English technical term as well as modern historiograpical concept.

WHile the entry of 1052 (1051) in Anglo-Saxon Chronicle Manuscript D (Worcester MS) certainly states that King Edward abolished heregeld established in the reign of King Æthelred II (978-1013) 39 years ago [i.e. about 1012 CE], the latest translation by Swanton translated the passage in question as following, as he avoided the use either of heregeld or of Danegeld altogether:

'And in the same year King Edward abolished that raider-tax (heregeld) which King Æthelred had earlier established; that was in the thirty-ninth year since he had begun it. That tax oppressed the whole English nation for as long a period as it is here written above; it always came before other taxes which were variously paid, and oppressed men in manifold ways' (Swanton trans. 2000: 173).

Then, which term was used by the scribe of ASC MSs to denote this new taxing system during the reign of King Æthelred?

'1011 (MS E): Here in this year the king [Æthelred] and his councillors sent to the raiding-army, and begged peace, and promised them tax (gafol) and provisions on condition that they leave off their raiding....... All these misfortunes befell us through lack of decision, in that they were not offered tax (gafol) in time; but when they had done great evil, then a truce and peace was made with them. And Nonetheless for all this truce and peace and tax (gafole<gafol), they travelled about everywhere in bands and raided and roped up and killed our wretched people......' (Swanton trans. 2000: 141).

The scribe here repeatedly employs the OE word gafol, 'tax, tribute' to designate the payment to the Danes, neither heregeld nor Danegeld. So, you might wonder where these two words came from, and why the scribe had not employed these new terms?

In the seminal understanding by Simon Keynes, he distinguishes the original (contemporary, in a sense of 11th century) as following (Keynes 1999; 235):

• The actual payment of the tribute to the Danes/ Vikings was called gafol, not heregeld.
• Heregeld was a name of the new Anglo-Saxon kingdom-wide taxation on landowners in the kingdom, whose amount of raised money should have originally been assigned specially for the payment of this kind of tribute/payment (gafol) to the Danes, but turned later also into other purposes.
• Danegeld was originally a moniker of the second, heregeld, thus the name of the taxation system.

In 19th century and at least until about the middle of the 20th century, however, some historians and translators also employed the term Danegeld not as a moniker of the taxation system, but as much wider connotation, the payment of the tribute to the Viking raiders in general (even sometimes those who primarily harassed the Frankish kingdoms), thus mixed the original source language with the historiographical concept. A few scholars even vehemently oppose the use of Danegeld as a historiographical concept to denote the payment to the Viking in general, but this kind of use is so widespread that it is not so easy to avoid the term.

Anyway, this confusion has not entirely cleared up even now, especially in old, copyright-free sources as well as in popular history material.

References:

• Two of Saxon chronicles parallel, vol. 1, ed. Charles Plummer and John Earle. London, 1892.
• Swanton, Michael. The Anglo-Saxon Chronicles: New Edition. London: Phoenix Pr., 2000 (1996).

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• Lapidge, Michael et al. (eds.). Blackwell Encyclopeadia of Anglo-Saxon England. Blackwell-Wiley: Oxford, 1999, p. 235, s.v. Heregeld ('army-tax') by Simon Keynes.