The relevant dimension here is probably what F. E. Smith, Lord Birkenhead, referred to as a "controlled" versus an "uncontrolled" constitution. He used this terminology when analyzing the constitution of Queensland for the Privy Council in McCawley v The King [1920] AC 691. That was an appeal from the High Court of Australia concerning a Queensland statute creating a Court for Industrial Arbitration and providing that its judges would also sit on the Supreme Court. It therefore conflicted with the Constitution Act 1867 (of Queensland) which had its own rules about Supreme Court membership and tenure. Lower courts had decided that the 1867 Act had a special status that could not be overridden by an ordinary Act (but could perhaps be subject to a two-step amendment process). The Privy Council decision was that on its construction, although the Act concerned the constitution, there was no mandate for reading any provisions into it about entrenchment. Rather, the Act itself contained the power "to make laws [...] in all cases whatsoever" (s.2), regarding which Lord Birkenhead remarked "it would be almost impossible to use wider or less restrictive language". That was also consistent with the general scheme of colonial legislation post-1865, where legislatures were endowed with plenary power over themselves and their local courts.
The Queensland constitution (as it then was) can be reckoned as codified but uncontrolled - in contrast to the British uncodified-uncontrolled, or the American codified-controlled. Lord Birkenhead's description shows that although this one was largely contained in a single document, unlike the British constitution, they both shared the quality that they could be amended at will by an ordinary act of the legislature.
Some communities and
notably Great Britain have not in the framing of constitutions felt it necessary or
thought it useful to shackle the complete independence of their successors. They have
shrunk from the assumption that a degree of wisdom and foresight has been conceded
to their generation which will be or may be, wanting to their successors in spite of the
fact that those successors will possess more experience of the circumstances and
necessities amid which their lives are lived. Those constitution-framers who have
adopted the other view must be supposed to have believed that certainty and stability
were in such a matter the supreme desiderata. Giving effect to this belief they have
created obstacles of varying difficulty in the path of those who would lay rash hands
upon the ark of the constitution. [...]
Many different terms have been employed in the text books to distinguish these two contrasted forms of constitution. Their special qualities may perhaps be exhibited as clearly by calling the one a controlled and the other an uncontrolled constitution as by any other nomenclature. Nor is a constitution debarred from being reckoned as an uncontrolled constitution because it is not like the British constitution constituted by historic development but finds its genesis in an originating document which may contain some conditions which cannot be altered except by the power which gave it birth. It is of the greatest importance to notice that where the constitution is uncontrolled the consequences of its freedom admit of no qualification whatever. The doctrine is carried to every proper consequence with logical and inexorable precision.
Uncodified constitutions are rare these days so it's hard to think of an example of a body of constitutional law that's uncodified (not written down in a single document) but also controlled (the legislative body doesn't have a completely free hand). Perhaps the canon law of the Catholic Church, prior to codification in 1917, would be an example: it was a sprawling body of texts, and while a Pope could formally promulgate new law at will, the interpretation of canon law is still subject to a fixed theological context. We might also count Israel since it has a partially-completed written constitution, which contains some entrenchment provisions in its finished parts - but if they ever finish then it would ipso facto be a codified constitution.
Finally, the actual ease of amendment is a political question. The cited example of India is a constitution that's very frequently amended, even though there are procedural hurdles. The United States has similar hurdles but amendments are much rarer in practice.