Collins Cobuild (Chapter 1, Section 8) distinguishes three underlying patterns for the verb + to-infinitive string:
8 V to-inf: The verb is followed by a to-infinitive.
This pattern has three structures:
• Structure I: Verbs in phase The number of victims continues to
• Structure II: Verb with Object He expects to fly to Beijing
• Structure III: Verb with Adjunct He hurried to catch up with
his friend. [note that this is not the in-order-to 'to']
In the meantime we wait to see what he will do.
Perhaps the simplest way to explain the distinctions is to start with their 'Structure III'. Notice that 'He hurried' is a bona-fide (if on occasion stylistically awkward) sentence, hence 'to ...' is arguably an adjunct. Neither 'to rise' in the first example, nor 'to fly to Beijing' in the second, can be sensibly dropped.
Next, Structure I involves 'verbs in phase', two verbs being needed to describe what is essentially one event / state. Cobuild lists the following 'meaning groups':
(1) begin (/stop ... / grow) // (2) appear // (3) try // (4) manage // (5) fail // (6) regret to say // (7) hasten // (8) chance // (9) tend (and adds good examples of each class; some multi-word verbs are included).
Lastly, Structure II involves verbs obviously associable but describing two distinct events / processes / states. Again, Cobuild lists the following 'meaning groups': (1) promise // (2) demand // (3) hope // (4) like // (5) claim // (6) need.
According to this classification, "The mayor vowed to reduce crime" is a direct-object construction, 'vow' being in the 'promise' group.
"We must all strive to do better" is a phase structure, 'strive' being in the 'try' group.