Cotes of Woodcote or Hanslope?

[Taylor94]

Was it usual for a junior line to adopt a completely different coat of arms but still retain a similar crest? By either adoption or by grant?

I have a John Cotes of Aylestone and Cossington, Leicestershire. Gentleman. Who as per the visitation of Leicestershire 1619. Lists the arms and crest as -
Crest - 'A Cock Or, Wattled Gules'
Arms - 'Argent, A Fret Azure, On A Canton Or, A Lion Rampant Sable'
This is unusual as this line claims descent from the Cotes of Woodcote.
Via this line as stated by Nichols and research seen online.

John Cotes of Aylestone and Cossington. Gent c1535-1603
Son of -
Alexander Cotes of Withington, Staff. Gent c1505-1570
Son of -
John Cotes of Prestwood and Norbury, Staff. Gent c1475-1538
Son of -
John Cotes of Woodcote, Shrop. Gent. c1450-1518
Son of -
John Cotes of Woodcote, Shrop. Esquire and Elizabeth Downton.

The ''John, son of John Cotes and Elizabeth Downton'' as per the visitation of shropshire 1623 is listed to have died without issue
This line uses the arms and crest -
Crest - 'A cock proper, beaked, combed, and legged or'
Arms -  'Quarterly, 1st and 4th, erm., 2nd and 3rd, paly of six or and gu.'
These are the arms of the Knightley family who married into the Cotes in the 1300s but the Cotes family adopted them in the 1500s. The original arms were' Argent a Cock Gules combed' Which were changed to the crest to a degree.

The arms and crest used by the Aylestone and Cossington Cotes are exactly the same as the ones used by the branch of Cotes living at Hanslope, Buckinghamshire in the 1500s early 1600s
These descend from another son of John Cotes and Elizabeth Downton called Thomas.
Thomas had 2 sons as per the shropshire visitation. A Richard who heads the Hanslope line and a John who is just listed as of 'Kirkstall Abbey' and no descent is given for him except 'fuit senescallus ib'm' Seneschal of Kirkstall Abbey?

It would seem the Cotes have the same arms as the Hanslope so likely have a link to this line although I cant seem to see it. The Hanslope line also uses the name Alexander.

[KGarrad]

It was more usual for a junior line to retain the arms, possibly differenced, and change the entire crest.

Remember that arms are granted to a named individual, not a family name, and are usually passed down to sons.

[Taylor94]

I'm familiar with how arms descend and how they are granted, but this is an odd scenario.
2 Lines of purportedly the same family are using completely different coats of arms from the main line whilst seemingly having no connection to each other via visitation pedigrees other than descending from 2 brothers, one of who is listed as having no issue but then claimed to have had a son called Alexander.

I know for certain that John Cotes of Aylestone and Cossington is using these arms ('Argent, A Fret Azure, On A Canton Or, A Lion Rampant Sable' although sometimes its stated as 'Fretty') as his daughter Katherine marries Roger Rowe, Esq of Youlgreave and London and on Roger's mural the Rowe arms are impaling Cotes.

I suppose this rests on whether that son John Cotes did die without issue as stated on Visitation. 2 researched pedigrees I've seen involving fairly good research hints that this isn't true but this doesn't explain how 2 different lines are using the same arms and descend potentially from 2 brothers who haven't differenced the original arms and have either adopted the same arms or both granted the same.

One pedigree hints the Cotes of Aylestone don't descend from Woodcote branch as the arms are different but this is the only verdict they give, solely based on that claim.
The Cotes of Aylestone pedigree given in the Leicester visitation 1619 and by more research done by Nichols for his antiquities of Leicestershire series seem to back up the claim to the Woodcote descent.